List of top Mathematics Questions on Trigonometry

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:

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:

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

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

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

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

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

If \(\frac{\sec \alpha}{\csc \beta} = p\) and \(\frac{\tan \alpha}{\csc \beta} = q\), then prove that \((p^2 - q^2) \sec^2 \alpha = p^2\).

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

If 2 sin A = 1, then the value of tan A + cot A is :

If tan A = \(\frac{4}{3}\), find sin A and cos A.

\(\frac{1 + \tan^2 A}{1 + \cot^2 A}\) equals to:

If \(2\tan A = 3\), then value of \(\sec A\) equals

Prove that : \(\sqrt{\frac{1 + \sin A}{1 - \sin A}} = \sec A + \tan A\).

Evaluate : \(\frac{3 \cos^2 30^{\circ} - 6 \csc^2 30^{\circ}}{\tan^2 60^{\circ}}\).

Prove that : \(\frac{1}{\sec x - \tan x} - \frac{1}{\cos x} = \frac{1}{\cos x} - \frac{1}{\sec x + \tan x}\)

If \( \tan \theta + \frac{1}{\tan \theta} = 2 \), find the value of \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).

Prove that : \( \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} = \sec \theta - \tan \theta \)

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

If \( \frac{\sec \alpha}{\text{cosec} \beta} = p \) and \( \frac{\tan \alpha}{\text{cosec} \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).

Given that \(\sin \theta = a/b\), then \(\cos \theta\) is equal to :

If \(\cos A = 1/2\), then the value of \(\sin^2 A + \cos^2 A\) is :