Trigonometric Identities

The value of $\sin12^\circ\sin48^\circ\sin54^\circ$ is

If $(1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n$, then the value of $n$ is

If $\cos\alpha+\cos\beta=a$, $\sin\alpha+\sin\beta=b$ and $\theta$ is the arithmetic mean between $\alpha$ and $\beta$, then $\sin2\theta+\cos2\theta$ is equal to

If $A = \cos^2\theta + \sin^4\theta$, then for all values of $\theta$:

If $\sin x,\ \cos x,\ \tan x$ are in GP, find $\cot 6x - \cot 2x$.

$ \displaystyle \text{The value of } \frac{1 - \tan^{2} 15^\circ}{1 + \tan^{2} 15^\circ} \text{ is:} $

The general solution of $ \sqrt{3}\cos x + \sin x = 3 $ is:

If $ \displaystyle \tan \theta = \frac{b}{a} $, then the value of $ a\cos 2\theta + b\sin 2\theta $ is

The value of $ \sin 30^\circ \cos 45^\circ + \cos 30^\circ \sin 45^\circ $

If $tan\alpha=\frac{m}{m+1}$ and $tan\beta=\frac{1}{2m+1}$ then $\alpha+\beta$ is equal to

If $\sin x + \sin^{2}x = 1$, then $\cos^{2}x + \cos^{4}x$ is equal to.

The value of $\tan\theta+2\tan2\theta + 4\tan4\theta + 8\cot8\theta$ is

If $sin x + a cos x = b$, then what is the expression for $|a sin x – cos x|$ in terms of $a$ and $b$?

The value of sin 20° sin 40° sin 80° is

If tan A - tan B = x and cot B - cot A = y, then cot (A - B) is equal to

If $sin x + a cos x = b$, then $|a sin x - cos x|$ is:

The value of tan 1° tan 2° tan 3° ... tan 89° is:

The value of $tan(\frac{7\pi}{8})$ is

If $0 < x < \pi $ and $cos x + sin x = \frac{1}{2}$ , then the value of tan x is

If $P=sin^{20} \theta + cos^{48} \theta $ then the inequality that holds for all values of is

If $a+b+c=\pi$ , then the value of $\begin{vmatrix} sin(A+B+C) &sinB &cosC \\ -sinB & 0 &tanA \\ cos(A+B)&-tanA &0 \end{vmatrix}$ is

Express (cos 5x – cos7x) as a product of sines or cosines or sines and cosines,

If tan x = - 3/4 and 3π/2 < x < 2π, then the value of sin2x is

The $sin^2 x tanx + cos^2 x cot x-sin2x=1+tanx+cotx $, $x \in (0 , \pi)$, then x

The value of sin 10°sin 50°sin 70° is

If cos x = tan y , cot y = tan z and cot z = tan x, then sinx =

Find the value of sin 12°sin 48°sin 54°

If $3 sin x + 4 cos x = 5$, then $6tan\frac{x}{2}-9tan^2\frac{x}{2}$

In a triangle ABC, $a\cos ^2\frac{C}{2}+\, c\, \, {\cos }^2\frac{A}{2}=\frac{3b}{2}$ then the sides of the triangle are in

The value of $\tan 9{^{\circ}}-\tan 27{^{\circ}}-\tan 63{^{\circ}}+\tan 81{^{\circ}}$ is equal to

If $y={\tan }^{-1}\lgroup{\frac{3x-{x}^3}{1-3{x}^2}}\rgroup\, ,\, \frac{-1}{\sqrt[]{3}}{\lt}x{\lt}\frac{1}{\sqrt[]{3}}$ then $\frac{dy}{dx}$ is

In a ΔABC, if $\tan ^2\frac{A}{2}+\tan ^2\frac{B}{2}+\tan ^2\frac{C}{2}=k$ , then k is always