Embibe Experts Solutions for Chapter: Trigonometric Ratios and Identities, Exercise 1: AMU-AT (B.Tech.) 2017

The value of $\cot 70°+4\cos 70°$ is

The equation $\sin x+\sin y+\sin z=-3$ for $0\le x\le 2\pi ,0\le y\le 2\pi ,0\le z\le 2\pi$ has

Let $A, B$ and $C$ are the angles of a plain triangle and $\tan \left(\frac{A}{2}\right)=\frac{1}{3}, \tan \left(\frac{B}{2}\right)=\frac{2}{3}$ Then, $\tan \left(\frac{C}{2}\right)$ is equal to

If $\alpha , \beta \left(\alpha \ne \beta \right)$ satisfies the equation $a\cos \theta +b\sin \theta =c,$ then the value of $\tan \left(\frac{\alpha +\beta }{2}\right)$ is

Let $0<\alpha <\pi ,0<\beta <\pi$ and $\cos \alpha +\cos \beta -\cos (\alpha +\beta )=\frac{3}{2}.$ Then the relation between $\alpha$ and $\beta$ will be

Let $P=(\theta :\sin \theta -\cos \theta =\sqrt{2}\cos \theta \}$ and $Q=\{\theta :\sin \theta +\cos \theta =\sqrt{2}\sin \theta \}$ be two sets. Then,

If $\sin \left(\alpha +\beta \right)=1, \sin \left(\alpha -\beta \right)=\frac{1}{2},\alpha ,\beta \in \left[0,\frac{\mathrm{\pi }}{2}\right]$ then the value of  $\tan (\alpha +2\beta )\tan (2\alpha +\beta )$ is