Trigonometry Questions

The least value of cosθsinθ is:

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?

If μ=60
∘
, then sinμ+cos(90
∘
−μ)=

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?

If secA−tanA=x, then the value of x is

If cos(A−B)−cos(A+B)=x, then the value of x is

If sin(−
3
4π
​
)=x, then the value of x is

The value of cscθ[
1+cscθ
sinθ
​
+
sinθ
1+cscθ
​
]−2cot
2
θ is equal to:

If tan(−
3
5π
​
)=x, then the value of x is

If
1−sinA
cosAcotA
​
=x, then the value of x is

If sin(A/2)=x, then the value of x is

What is the value of sin
4
7π
​
?

cot
4
A+cot
2
A is equal to:

cos
3
A is equal to:

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
∘
?

If A is an acute angle, what is the value of cscA, if cotA=
p
2
−1
2p
​
?

What is the value of $\left(\cos 45^{\circ }+\frac{1}{3}\right)$?

Evaluate:
$${\left(\frac{\sin 23^{\circ }\cos 67^{\circ }+\cos 23^{\circ }\sin 67^{\circ }}{{\mathrm{cosec}}^{2}15^{\circ }-{\tan }^{2}75^{\circ }}\right)}^3$$

If 6cos
2
θ+cosθ=2, 0
∘
<θ<90
∘
, then the value of (cscθ+cotθ+tanθ) is:

If
secθ−tanθ
secθ+tanθ
​
=
3
5
​
, 0
∘
<θ<90
∘
, then what is the value of (cscθ+cosθ+cotθ)?

If $\frac{1}{1+\cos A}+\frac{1}{1-\cos A}=x$, then the value of $x$ is:

If
cos
2
Acos
2
B
sin
2
A−sin
2
B
​
=x, then the value of x is:

If sin60
∘
+cos45
∘
=x, then the value of x is:

$\Delta DEF$ is right-angled at $E$. If $\cos D=\frac{8}{17}$, then what is the value of $\sec F$?

If $\cos 45^{\circ }-\sec 30^{\circ }=x$, then the value of $x$ is:

△ABC is right angled at B. If secA=
3
5
​
, then what is the value of cosec C?

What is the value of (
3
1
​
−sec45
∘
)?

If cot(
2
A
​
)=x, then the value of x is:

If $\cot \left(\frac{A}{2}\right)=x$, then $x$ is equal to:

If $\cot 60^{\circ }+\csc 60^{\circ }=x$, then the value of $x$ is:

If $\sqrt{\frac{1-\cos A}{2}}=x$, then the value of $x$ is:

If $\sqrt{1+\sec A}=x$, then the value of $x$ is:

If tan(
2
A
​
)=x, then the value of x is:

If sec(−
4
5π
​
)=x, then the value of x is:

If 2secA−
cosA
1+sinA
​
=x, then the value of x is:

If cos60
∘
−sec30
∘
=x, then the value of x is:

If tan3θ=cot(θ−22
∘
), where 3θ is an acute angle, find the value of θ.

If cot(−
4
5π
​
)=x, then the value of x is:

If cos(
2
A
​
)=x, then the value of x is:

If 2csc
2
A=x, then the value of x is:

If tan(−
4
7π
​
)=x, then the value of x is:

If
cotB−cotA
cotAcotB+1
​
=x, then the value of x is:

If 2sec
2
A=x, then the value of x is:

If $2{\cos }^2\theta -5\cos \theta +2=0$, $0^{\circ }<\theta <90^{\circ }$, then the value of $\frac{1}{\csc \theta +\cot \theta }$ is:

If 4tanA=3, then cos
2
A−sin
2
A equals:

If cos
2
θ−sin
2
θ−3cosθ+2=0, 0
∘
<θ<90
∘
, then what is the value of
2
1+
5

​
cosθ+tanθ
​
?

Which of the following is NOT a correct formula?

If cos(
4
π
​
)−tan(
4
π
​
)=x, then x is:

If $\sqrt{\frac{1+\cos A}{2}}=x$, then find the value of $x$.

If $\tan 45^{\circ }+\text{cosec }30^{\circ }=x$, then find the value of $x$.

If sec(−
4
7π
​
)=x, then the value of x is:

If tan(
2
A
​
)=x, then the value of x is:

If (secA−tanA)
2
=x, then the value of x is:

What is the value of (
2
1
​
−cot45
∘
)?

In ΔABC, the measure of angle B is 90
∘
. If sinA=
25
24
​
and AB=1.4cm, then what is the length (in cm) of side BC?

One internal angle of a rhombus of side 12cm is 120
∘
. What is the length of its longer diagonal?

If
1+sinA
1−sinA
​
=x, then x is:

If $\sec A+\tan A=x$, then find the value of $x$.

If tanA=x, then x is:

In △PQR, the measure of angle Q is 90
∘
. If tanP=
3
4
​
and 1.5cm, then what is the length (in cm) of side PR?

△XYZ is right-angled at Y. If m∠Z=45
∘
, then find the value of (cscX−
3

​

2
​
).

If cos45
∘
−sec60
∘
=x, then the value of x is:

If
2
1+cosA
​
=x, then the value of x is:

If secA+tanA=x, then the value of x is:

If cscA−cotA=x, then the value of x is:

If
2
1−cosA
​
=x, then the value of x is: