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Trigonometry Questions

Practice 198 Trigonometry questions with detailed answers and explanations. Free MCQs, PYQs, and mock test questions for NEET, JEE, GATE, SSC and more.

📚
198
Total Questions
🟢
6
Easy
🟡
186
Medium
🔴
6
Hard
Practice by Exam:Quantitative Aptitude(143)Mathematics(52)Quantitative Aptitude@NUM: 68(1)Quantitative Aptitude@NUM: 64(1)Quantitative Aptitude@NUM: 66(1)

About Trigonometry — practice questions, PYQs & concepts

Trigonometry is a frequently-tested topic on Quantitative Aptitude, Mathematics, Quantitative Aptitude@NUM: 68. ExamTest.live currently lists 198 Trigonometry questions spanning previous-year papers from 2004 to 2026, each with worked solutions and a step-by-step explanation. Use the filters on this page to focus on a specific exam, difficulty level or year — every answer key is free, no sign-up required.

Trigonometry weight in competitive exams

Across our Trigonometry question bank, the largest sources are Quantitative Aptitude (143), Mathematics (52), Quantitative Aptitude@NUM: 68 (1), Quantitative Aptitude@NUM: 64 (1) and Quantitative Aptitude@NUM: 66 (1). Click any exam chip above to drill down to that exam-specific question set.

How to use this page

  • Start easy: 6 easy Trigonometry questions are available — build fluency before moving up.
  • Target weak years: Use the year filter to focus on the most recent 2026 paper or older PYQs you have not attempted.
  • Time yourself: Every question shows the average solve time so you can benchmark your speed against other students.
  • Read every explanation: Even on questions you got right — the explanation often surfaces a faster approach you can reuse.

All Trigonometry Questions(1–100 of 198)

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Q1hardmcqQuantitative AptitudeSSC Selection Post 2021 Matriculation Level2026
11% accuracy
If , , then what is the value of ?
Q2mediummcqMathematicsMathematics Mock Test - 62026
15% accuracy
If , then is equal to:
Q3mediummcqMathematicsMathematics Mock Test - 62026
7% accuracy
The solution set of the equation is:
Q4mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If , then the value of is:
Q5mediummcqQuantitative AptitudeCompetitive Exam2026
7% accuracy
Find the value of .
Q6mediummcqMathematicsMathematics Mock Test - 102026
25% accuracy
For , the value of is:
Q7mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
The maximum value of in the interval occurs at :
Q8mediummcqMathematicsMathematics Mock Test - 102026
8% accuracy
The value of is:
Q9mediummcqMathematicsMathematics Mock Test - 12026
8% accuracy
A line makes an angle , , with the , , and axes respectively. Then the value of is:
Q10mediummcqMathematicsMathematics Mock Test - 102026
0% accuracy
The value of so that decreases for all real values of is given by:
Q11mediummcqMathematicsMathematics Mock Test - 102026
17% accuracy
is equal to:
Q12mediummcqMathematicsMathematics Mock Test - 12026
0% accuracy
The function increases monotonically if:
Q13mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
If
(secA−1)
2

tan
2
A
​
=x, then the value of x is:
Q14mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
If tan(
2
A
​
)=x, then the value of x is:
Q15mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
If cot(−
3
4π
​
)=x, then the value of x is:
Q16hardmcqQuantitative AptitudeSSC CGL2026
25% accuracy
If cosθ=sin(2θ)

=0, what is the value of cos
4
θ+sin
4
θ+cos
3
θ+sin
3
θ+sin
2
θ+cos
2
θ+sinθ+cosθ?
Q17mediummcqQuantitative AptitudeSSC CGL2026
25% accuracy
The least value of cosθsinθ is:
Q18easymcqQuantitative AptitudeSSC CGL2026
0% accuracy
If μ=60
∘
, then sinμ+cos(90
∘
−μ)=
Q19mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
If cos(A−B)−cos(A+B)=x, then the value of x is
Q20mediummcqQuantitative AptitudeCompetitive Exam Practice2026
0% accuracy
Find cosθ using a right-angled triangle where the side opposite to angle θ (perpendicular) is 7 units and the side adjacent to angle θ (base) is 24 units.

image
Q21mediummcqMathematicsCompetitive Exam Practice2026
0% accuracy
The ratio of the length of a tree to its shadow is . The angle of the sun's elevation is:
Q22mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If cos2θ=0, where θ is an acute angle, then find the value of sin(75
∘
−θ).
Q23mediummcqQuantitative AptitudeSSC CGL2026
33% accuracy
If secA−tanA=x, then the value of x is
Q24mediummcqQuantitative AptitudeCompetitive Exam 20262026
0% accuracy
If sinθ+cscθ=5, then the value of sin
3
θ+csc
3
θ is:
Q25mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
The sides of a right-angled triangle, right-angled at B, are 6, 8 and 10 units. C is the vertex opposite to the side with length 8 units. What is the value of tan
2
A+cos
2
C?
Q26mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If sin(−
3
4π
​
)=x, then the value of x is
Q27mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
If , then the value of is:
Q28mediummcqMathematicsMathematics Mock Test - 52026
0% accuracy
The value of is:
Q29mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
In a triangle, the length of the side opposite the angle which measures 60
∘
is 6cm. What is the length of the side opposite to the angle which measures 90
∘
?
Q30mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If tan(−
3
5π
​
)=x, then the value of x is
Q31mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If sin(A/2)=x, then the value of x is
Q32mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
cot
4
A+cot
2
A is equal to:
Q33mediummcqQuantitative AptitudeSSC CGL2026
50% accuracy
cos
3
A is equal to:
Q34mediummcqQuantitative AptitudeSSC Selection Post 2018 Higher Secondary Level2026
0% accuracy
और है, तो
Q35mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If
1−sinA
cosAcotA
​
=x, then the value of x is
Q36mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If A is an acute angle, what is the value of cscA, if cotA=
p
2
−1
2p
​
?
Q37hardmcqQuantitative AptitudeSSC CGL2026
0% accuracy
The value of cscθ[
1+cscθ
sinθ
​
+
sinθ
1+cscθ
​
]−2cot
2
θ is equal to:
Q38mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
What is the value of sin
4
7π
​
?
Q39mediummcqMathematicsMathematics Mock Test - 42026
0% accuracy
The principal value of is:
Q40mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
Evaluate:
Q41mediummcqMathematicsAIEEE 20062026
0% accuracy
If the roots of the quadratic equation are and , respectively, then the value of is:
Q42mediummcqMathematicsAIEEE 20072026
0% accuracy
A tower stands at the centre of a circular park. and are two points on the boundary of the park such that subtends an angle of at the foot of the tower, and the angle of elevation of the top of the tower from or is . The height of the tower is:
Q43mediummcqQuantitative Aptitude@NUM: 68SSC CGL2026
0% accuracy
If , then is equal to:
Q44mediummcqMathematicsAIEEE 20072026
0% accuracy
If , then a value of is:
Q45mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
What are the principal solutions of the equation ?
Q46easymcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
What is the value of
Q47mediummcqQuantitative AptitudeCompetitive Exam2026
0% accuracy
If , then what is ?
Q48mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If then is:
Q49mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If 6cos
2
θ+cosθ=2, 0
∘
<θ<90
∘
, then the value of (cscθ+cotθ+tanθ) is:
Q50mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If
secθ−tanθ
secθ+tanθ
​
=
3
5
​
, 0
∘
<θ<90
∘
, then what is the value of (cscθ+cosθ+cotθ)?
Q51mediummcqMathematicsStaff Selection Commission2026
0% accuracy
2sec
2
A is equal to:
Q52mediummcqQuantitative AptitudeCompetitive Exam2026
100% accuracy
The value of is:
Q53mediummcqQuantitative Aptitude@NUM: 64SSC CGL2026
0% accuracy
If , then the value of is:
Q54mediummcqQuantitative Aptitude@NUM: 66SSC CGL2026
0% accuracy
If , then the value of is:
Q55mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , then the value of is:
Q56mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , then the value of is:
Q57mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If , then the value of is:
Q58mediummcqMathematicsAIEEE 20062026
0% accuracy
The number of values of in the interval satisfying the equation is:
Q59mediummcqMathematicsStaff Selection Commission2026
0% accuracy
What is the value of sin(
3
5π
​
)?
Q60mediummcqMathematicsStaff Selection Commission2026
0% accuracy
In a right-angled triangle, the length of the side opposite the right angle is 9
3

​
cm. What is the length of the side opposite to the angle which measures 30
∘
?
Q61mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
is equal to:
Q62mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
What is the value of ?
Q63mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If
cos
2
Acos
2
B
sin
2
A−sin
2
B
​
=x, then the value of x is:
Q64mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
is right-angled at . If , then what is the value of ?
Q65mediummcqQuantitative AptitudeStaff Selection Commission2026
0% accuracy
is equal to:
Q66mediummcqQuantitative AptitudeSSC CGL2026
100% accuracy
If sin60
∘
+cos45
∘
=x, then the value of x is:
Q67mediummcqMathematicsAIEEE 20062026
0% accuracy
The value of is:
Q68mediummcqMathematicsAIEEE 20062026
0% accuracy
A particle has two velocities of equal magnitude inclined to each other at an angle . If one of them is halved, the angle between the other and the original resultant velocity is bisected by the new resultant. Then is:
Q69mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
△ABC is right angled at B. If secA=
3
5
​
, then what is the value of cosec C?
Q70mediummcqQuantitative AptitudePrepp2026
0% accuracy
If , where is an acute angle, then find the value of .
Q71mediummcqQuantitative AptitudePrepp2026
0% accuracy
Simplify the following expression:
Q72mediummcqMathematicsMathematics Mock Test - 22026
0% accuracy
If and are two angles of a triangle, then what is the third angle?
Q73mediummcqQuantitative AptitudeSSC CPO 20242026
0% accuracy
If , then one of the values of the expression is _______.
Q74mediummcqMathematicsMathematics Mock Test - 92026
0% accuracy
If takes a non-positive permissible value, then will be:
Q75mediummcqQuantitative AptitudePrepp2026
0% accuracy
If , then find the value of .
Q76mediummcqMathematicsStaff Selection Commission2026
0% accuracy
cos3A is equal to:
Q77mediummcqQuantitative AptitudeSSC CGL2026
100% accuracy
What is the value of ?
Q78mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
What is the value of (
3
1
​
−sec45
∘
)?
Q79mediummcqQuantitative AptitudeSSC CGL2026
0% accuracy
If cot(
2
A
​
)=x, then the value of x is:
Q80mediummcqMathematicsAIEEE 20062026
0% accuracy
If and , then is:
Q81mediummcqQuantitative AptitudeCompetitive Exam2026
Find the value of (sin75
∘
+sin15
∘
).
Q82easymcqQuantitative AptitudeStaff Selection Commission2026
If 8tanA=5, what is the value of
8sinA+11cosA
8sinA−7cosA
​
?
Q83mediummcqQuantitative AptitudeCompetitive Exam2026
What is the value of ?
Q84mediummcqQuantitative AptitudePrepp2026
If , then the value of is _________.
Q85mediummcqMathematicsMathematics Mock Test - 82026
If , then
Q86mediummcqQuantitative AptitudePrepp2026
Find the value of .
Q87mediummcqQuantitative AptitudePrepp2026
If and , then find the value of .
Q88mediummcqMathematicsMathematics Mock Test - 82026
If , then the value of will be:
Q89mediummcqQuantitative AptitudePrepp2026
Find the value of .
Q90easymcqQuantitative AptitudeSSC CGL2026
Which of the following is NOT a correct formula?
Q91mediummcqQuantitative AptitudeCompetitive Exam Practice2026
If tanθ+cotθ=2, then find the value of tan
53
θ+cot
38
θ.
Q92mediummcqQuantitative AptitudeCompetitive Exam2026
In , the measure of angle is . If and , then what is the length (in ) of side ?
Q93mediummcqMathematicsAIEEE2026
If in a triangle , the altitudes from the vertices on opposite sides are in H.P., then are in:
Q94mediummcqQuantitative AptitudeCompetitive Exam Practice2026
If sinA+cosA=
3
4
​
, then find the value of tanA+cotA.
Q95mediummcqQuantitative AptitudeSSC CGL2026
If cos
2
θ−sin
2
θ−3cosθ+2=0, 0
∘
<θ<90
∘
, then what is the value of
2
1+
5

​
cosθ+tanθ
​
?
Q96mediummcqQuantitative AptitudeSSC CGL2026
If 4tanA=3, then cos
2
A−sin
2
A equals:
Q97mediummcqMathematicsAIEEE2026
is a vertical pole with at the ground level and at the top. A man finds that the angle of elevation of the point from a certain point on the ground is . He moves away from the pole along the line to a point such that . From , the angle of elevation of the point is . Then the height of the pole is:
Q98mediummcqQuantitative AptitudeSSC CGL2026
If , , then the value of is:
Q99mediummcqMathematicsAIEEE2026
If , then is equal to:
Q100mediummcqMathematicsAIEEE 20092026
Let and denote the statements: If , then:
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How many Trigonometry questions are on ExamTest.live?▼
We have 198 Trigonometry questions spread across 2 pages, covering easy, medium, and hard difficulty levels with detailed explanations.
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Trigonometry questions are commonly asked in Quantitative Aptitude, Mathematics, Quantitative Aptitude@NUM: 68, Quantitative Aptitude@NUM: 64, Quantitative Aptitude@NUM: 66. You can filter by exam using the links above.
How do I practice Trigonometry questions effectively?▼
Start with easy questions to build confidence, then tackle medium and hard ones. Use the filter buttons to sort by difficulty. Reveal the answer only after attempting each question, and read the explanation thoroughly.