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