List of top Mathematics Questions on Trigonometry

Let $K = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$ then the value of $\sin \left( 10K \frac{\pi}{3} \right)$ is :

Let $x \in [-\pi, \pi]$ & $S = \{ x : \sin x (\sin x + \cos x) = a, a \in I \}$, then number of elements in set $S$ is equal to :

If $\tan \theta = 1$, then $\theta = $:

Value of $\sin^2\theta + \cos^2\theta$:

If \[ \frac{\tan(A-B)}{\tan A}+\frac{\sin^2 C}{\sin^2 A}=1, \quad A,B,C\in\left(0,\frac{\pi}{2}\right), \] then:

Given cot \(\theta\) = 3, the value of cos \(\theta\) is :

The least value of $(\cos^2 \theta - 6\sin \theta \cos \theta + 3\sin^2 \theta + 2)$ is

In \(\Delta ABC\) if \(\frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1\) where \(A, B, C \in (0, \frac{\pi}{2})\) then

Let \( \dfrac{\pi}{2} < \theta < \pi \) and \( \cot \theta = -\dfrac{1}{2\sqrt{2}} \). Then the value of \[ \sin\!\left(\frac{15\theta}{2}\right)(\cos 8\theta + \sin 8\theta) + \cos\!\left(\frac{15\theta}{2}\right)(\cos 8\theta - \sin 8\theta) \] is equal to

Let \( y = y(x) \) be the solution of the differential equation \( x^2 dy + (4x^2 y + 2\sin x)dx = 0 \), \( x>0 \), \( y\left(\frac{\pi}{2}\right) = 0 \). Then \( \pi^4 y\left(\frac{\pi}{3}\right) \) is equal to :

The value of \( \csc 10^\circ - \sqrt{3}\sec 10^\circ \) is:

Evaluate the limit: \[ \lim_{x \to 0} \frac{\sin(2x) - 2\sin x}{x^3} \]

The value of \(\text{cosec}10^\circ - \sqrt{3} \sec10^\circ\) is equal to:

The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPRSTUVP, is :

The angles of depression of the top and the bottom of a 6 m high building from the top of a multi-storeyed building are 30° and 60° respectively. Find the height of the multi-storeyed building and the distance between the two buildings.

OR

Two poles of equal heights are standing opposite each other on either side of the road, which is 60 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60°, respectively. Find the height of the poles and the distances of the point from the poles.

In triangle $ABC$ if $\angle B = 90^\circ$, $AB = 5$ cm and $BC = 12$ cm, the value of $\sin A$ will be :

If tan A = √3, then the value of Sec A will be :

If \(\sin x = p\), then prove that : (i) \(\cot x = \frac{\sqrt{1 - p^2}}{p}\) (ii) \(\frac{1 + \tan^2 x}{1 + \cot^2 x} = \frac{p^2}{1 - p^2}\)

Let \(\tan \left( \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{2}{3} \right) + \tan \left( \frac{\pi}{4} - \frac{1}{2} \sin^{-1} \frac{2}{3} \right) = k\). Then number of solution of the equation \(\sin^{-1}(kx - 1) = \sin x - \cos^{-1} x\) is/are :

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

If \[ k=\tan\!\left(\frac{\pi}{4}+\frac{1}{2}\cos^{-1}\!\left(\frac{2}{3}\right)\right) +\tan\!\left(\frac{1}{2}\sin^{-1}\!\left(\frac{2}{3}\right)\right), \] then the number of solutions of the equation \[ \sin^{-1}(kx-1)=\sin^{-1}x-\cos^{-1}x \] is:

Evaluate: \(\frac{5 \cos^2 60^\circ + 4 \sec^2 30^\circ - \tan^2 45^\circ}{\sin^2 30^\circ + \cos^2 30^\circ}\)

Prove that: \(1 + \frac{\cot^2 \alpha}{1 + \csc \alpha} = \csc \alpha\)

Prove that: \(\frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{\csc^3 \theta}{\csc^2 \theta - 1} = \sec \theta \cdot \csc \theta (\sec \theta + \csc \theta)\)