Embibe Experts Solutions for Chapter: Trigonometric Ratios, Functions and Identities, Exercise 2: Exercise-2

If $3\sin \beta =\sin \left(2\alpha +\beta \right)$, then $\tan \left(\alpha +\beta \right)-2\tan \alpha$ is

If $\alpha +\beta +\gamma =2\pi$, then

If $x+y=z,$ then ${\cos }^{2}x+{\cos }^{2}y+{\cos }^{2}z-2\cos x\cos y\cos z$ is equal to

Which of the following values of $\text{'}t\text{'}$ may satisfy the condition $2\sin t=\frac{1-2x+5x^2}{3x^2-2x-1}, t\in \left[-\frac{\pi }{2},\frac{\pi }{2}\right]$.

$\sin x+\sin 2x+\sin 3x=0$ if

$\cos 4x\cos 8x-\cos 5x\cos 9x=0$ if

If the equation $\sin \left(\pi x^2\right)-\sin \left(\pi x^2+2\pi x\right)=0$ is solved for positive roots, then in the increasing sequence of positive root

$4{\sin }^{4}x+{\cos }^{4}x=1$ if