List of top Mathematics Questions on Trigonometric Identities asked in AP EAPCET

The value of \[ \sin20^\circ\sin40^\circ\sin80^\circ \] is:

If \[ \sin\theta+\cos\theta=\sqrt{2}\cos\alpha, \] where \(0<\theta<\frac{\pi}{2}\), then the value of \[ \sin2\theta \] is:

If \[ \tan\theta+\cot\theta=4, \] then the value of \[ \sec^2\theta+\csc^2\theta \] is:

The value of \[ \sin^2 15^\circ+\cos^2 15^\circ \] is

If \[ \sin\theta+\cos\theta=1, \] then the value of \[ \sin\theta\cos\theta \] is:

Simplify: \[ \frac{1}{1+\sin\theta}+\frac{1}{1-\sin\theta}= \]

Simplify: \[ \frac{\cos x}{1+\sin x}+\tan x= \]

If \(\theta\) is any angle, then \[ \sin^2\theta \cos^2\theta= \]

Evaluate: \[ (4\cos^2 9^\circ-3)(4\cos^2 27^\circ-3)= \]

In a triangle \(ABC\), \[ \tan \frac{A}{2}\tan \frac{B}{2} +\tan \frac{B}{2}\tan \frac{C}{2} +\tan \frac{C}{2}\tan \frac{A}{2} = \]

Simplify \[ \sec^2 x+5\tan x+5= \]

Let \(\alpha,\beta\) be two real numbers such that \[ \pi\lt (\alpha-\beta)\lt 3\pi. \] If \[ \sin\alpha+\sin\beta=-\frac{21}{65} \] and \[ \cos\alpha+\cos\beta=-\frac{2}{65}, \] then \[ \cos\left(\frac{\beta-\alpha}{2}\right)= \]

A true statement among the following identities is:

If \[ \sin\theta+\cosec\theta=4, \] then \[ \sin^2\theta+\cosec^2\theta= \]

If \[ \sin^4\theta \cos^2\theta=\sum_{n=0}^{\infty} a_{2n}\cos 2n\theta, \] then the least \(n\) for which \[ a_{2n}=0 \] is

Evaluate \[ 1+\sec^2x\sin^2x= \]

A true statement among the following identities is