Embibe Experts Solutions for Chapter: Trigonometric Ratios and Identities, Exercise 1: Assam CEE 2016

The value of $\frac{{\alpha }^3}{2}{cosec}^2\left(\frac{1}{2}{\tan }^{-1}\frac{\alpha }{\beta }\right)+\frac{{\beta }^3}{2}{\sec }^2\left(\frac{1}{2}{\tan }^{-1}\frac{\beta }{\alpha }\right)$ is equal to:

The graph of the function $y=\cos x.\cos \left(x+2\right)-{\cos }^2\left(x+1\right)$ is

If $\tan \alpha$ equals the integral solution of the inequality $9x^2-51x+70<0$ and $\tan \beta$ be the slope of the bisector of the first quadrant, then $\sin 2\alpha +\cos 2\beta$ is equal to

If $\sum _{x=0}^{2016}\sin \frac{\pi r}{3}=k$, then the value of $\sum _{x=0}^{2016}{\sin }^3\frac{\pi r}{3}$ is equal to

In a triangle $ABC$, if $A:B:C=1:2:4$, then $\sec A\sec B\sec C$ is equal to

If $\cos A\cos B\cos C=-\frac{1}{2}$ and $A=C$ in a triangle $ABC$ then $\cos 2A$ is equal to

The number of solutions of the equation $\left|\cot x\right|=\cot x+\frac{1}{\sin x},0\le x\le 2\pi$