List of top Mathematics Questions on Trigonometric Identities

If \(A\) and \(B\) are the minimum and maximum values of \[ \sin^6 x+\cos^6 x, \] then \(A+B=\)

Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

For an acute angle $\theta$, if $\sin \theta = \frac{1}{9}$, then value of $\frac{9\csc\theta + 1}{9\csc\theta - 1}$ is

Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is

Prove that : $(1 + \cot \theta - \csc \theta)(1 + \tan \theta + \sec \theta) = 2$

Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is

Prove that: $\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta$

Simplest form of $\frac{\sec A}{\sqrt{\sec^2 A - 1}}$ is

For an acute angle $\theta$, if $\sin\theta = \frac{1}{9}$, then value of $\frac{9\csc\theta + 1}{9\csc\theta - 1}$ is

If sec \(\theta\) + tan \(\theta\) = m, show that \(\frac{m^2 - 1}{m^2 + 1} = \sin \theta\).

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

\(\frac{\sec^2 A - 1}{\sin^2 A}\) is same as

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

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

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

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

If \(\cos A + \sin A = \sqrt{2} \cos A\), prove that \(\cos A - \sin A = \sqrt{2} \sin A\).

\(\sin 2 \theta = 2 \sin \theta\) is true, when \(\theta\) is equal to

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

Given that $\sin\theta = \frac{a}{b}$, then $\cos\theta$ is equal to :

Evaluate \[ \frac{\cos\theta}{1-\cos\theta} + \frac{\sec\theta}{1+\sec\theta}. \]

Prove that : (sin A + sec A)\(^2\) + (cos A + cosec A)\(^2\) = (1 + sec A cosec A)\(^2\)

If sin \(\theta\) + cos \(\theta\) = \(\sqrt{3}\), then prove that tan \(\theta\) + cot \(\theta\) = 1.

Solve any one of the following internal choices (a) or (b):
26(a) If $\sin \theta + \cos \theta = \sqrt{3}$, then prove that $\tan \theta + \cot \theta = 1$.

If \(\cos \theta + \sin \theta = \sqrt{2} \cos \theta\), then prove that \(\cos \theta - \sin \theta = \sqrt{2} \sin \theta\).