Trigonometry Questions

Find the value of $\frac{\cos 25^{\circ }-\sin 65^{\circ }}{\cos 25^{\circ }+\sin 65^{\circ }}$.

If $\sin (5x-40^{\circ })=\cos (5y+40^{\circ })$, then the value of $x+y$ is:

If cos2θ=0, where θ is an acute angle, then find the value of sin(75
∘
−θ).

If sinθ+cscθ=5, then the value of sin
3
θ+csc
3
θ is:

The ratio of the length of a tree to its shadow is $1:\frac{1}{\sqrt{3}}$. The angle of the sun's elevation is:

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.

The value of $\csc 41^{\circ }-\sec 49^{\circ }$ is:

What is the value of $\cos 1^{\circ }\cdot \cos 2^{\circ }\cdot \cos 3^{\circ }\dots \cos 177^{\circ }\cdot \cos 178^{\circ }\cdot \cos 179^{\circ }$

If $\tan \theta +\sec \theta =a$, then what is $\sec \theta$?

In a right-angled triangle $XYZ$, $\angle Y=90^{\circ }$. If $XY=2\sqrt{6}$ and $XZ-YZ=2$, then the value of $\sec X+\tan X$ is:

If $\cot \left(-\frac{4\pi }{3}\right)=x$, then the value of $x$ is:

If $\tan \left(\frac{A}{2}\right)=x$, then the value of $x$ is:

Find the angle of elevation of the Sun when the length of the shadow of a vertical pole is $\sqrt{3}$ times its height.

If $\sin \theta =\frac{5}{13}$, then what is the value of $\tan \theta +\sec \theta$?

If $\cot \theta =\frac{x}{y}$, then what is the value of $\frac{x\cos \theta -y\sin \theta }{x\cos \theta +y\sin \theta }$?

Find the minimum value of $5\sin \theta +12\cos \theta$.

If the length of the shadow on the ground of a post is $\frac{1}{\sqrt{3}}$ times its height, the angle of elevation of the Sun is:

If cosec
−1
(
6
11π
​
)=x, then what is the value of x?

If $\frac{{\tan }^{2}A}{(\sec A-1{)}^2}=x$, then the value of $x$ is:

If $\sin \theta =\frac{5}{13}$, then what is the value of $\tan \theta +\sec \theta$?

Find the angle of the elevation of the Sun when the length of shadow of a vertical pole is $\sqrt{3}$ times its height.

Find the minimum value of $5\sin \theta +12\cos \theta$.

If the length of shadow on the ground of a post is $\frac{1}{\sqrt{3}}$ times of its height, the angle of elevation of the Sun is:

If $\csc \theta +\cot \theta =\sqrt{3}$, find the value of $\csc \theta$.

If $\sec \theta =\csc \varphi$ and $0^{\circ }<(\theta ,\varphi )<90^{\circ }$, then the value of $\sin (\theta +\varphi )$ is:

In $△ABC$, $\angle B=90^{\circ }$, $BC=7\text{cm}$. If $AC-AB=1\text{cm}$, then the value of $\sin A$ (denoted here as $\sin \theta$ for the targeted angle) is:

An arc of length $121\text{cm}$ subtends an angle of $77^{\circ }$ at the centre of a circle. The radius of the circle is:

In $△DEF$, the measure of angle $E$ is $90^{\circ }$. If $\cos D=\frac{5}{13}$ and $DE=1\text{cm}$, then what is the length (in $\text{cm}$) of side $EF$?

If 3sec
4
θ+8=10sec
2
θ, then the value of tanθ can be:

The expression sin
2
θ+cos
2
θ−1=0 is satisfied by how many values of θ?

Find the value of (sin75
∘
+sin15
∘
).

If tanθ+cotθ=2, then find the value of tan
53
θ+cot
38
θ.

If sinA+cosA=
3
4
​
, then find the value of tanA+cotA.

If 4sin
2
θ−4
3

​
sinθ+3=0, then find the value of θ (0
∘
<θ<90
∘
).

The chord of a circle is $10\text{cm}$ in length and at a distance of $\frac{10}{\sqrt{3}}\text{cm}$ from the centre. Calculate the angle subtended by the chord at the centre of the circle.

What is the value of $\left(\csc 60^{\circ }+\frac{1}{2}\right)$?

If $3\sin \alpha +5\cos \alpha =5$, then the value of $(3\cos \alpha -5\sin \alpha {)}^2$ is equal to

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

If
1−tanAtanB
tanA+tanB
​
=x, then the value of x is:

If
cscA−cotA
1
​
=x, then the value of x is:

If Psin60
∘
=Qcsc45
∘
, then the value of
P
2
−Q
2

P
2
+Q
2

​
is equal to:

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

If $\tan 2\theta \tan \theta =1$, then the value of $\tan 2\theta$ is:

If $\tan \theta +\sin \theta =m$ and $\tan \theta -\sin \theta =n$, then which one of the following relations is correct?