Prove that $\sin (n+1) x \sin (n+2) x+\cos (n+1) x \cos (n+2) x=\cos x$
If $\cos x + {\cos ^2}x = 1,$ then the value of ${\sin ^2}x + {\sin ^4}x$ is
At what time between $10\,\,O'clock$ and $11\,\,O 'clock$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?
The value of the expression $1 - \frac{{{{\sin }^2}y}}{{1 + \cos \,y}} + \frac{{1 + \cos \,y}}{{\sin \,y}} - \frac{{\sin \,\,y}}{{1 - \cos \,y}}$ is equal to
The value of $\tan ( - 945^\circ )$ is
If $\tan \theta - \cot \theta = a$ and $\sin \theta + \cos \theta = b,$ then ${({b^2} - 1)^2}({a^2} + 4)$ is equal to