Embibe Experts Solutions for Chapter: Trigonometric Equations, Exercise 1: TS EAMCET 2021 (04-Aug Shift-2)

The equation ${\sin }^{4}x-\left(k+3\right){\sin }^{2}x-k-4=0$ has a solution if

Number of solutions of the equation $\sin x-\sin 2x+\sin 3x=2{\cos }^{2}x-2\cos x$ in $\left(0,\pi \right)$ is

The general solution of $\cos 2x-2\tan x+2=0$ is

If $\cos \theta =-\frac{1}{\sqrt{2}}$ and $\tan \theta =1,$ then the general value of $\theta$ is

The value of $\left(1-\mathrm{cos\theta }\right)\left(1+\mathrm{cos\theta }\right)\left(1+{\cot }^2\mathrm{\theta }\right)$, when $\theta =\frac{\pi }{15}$ is

The number of solutions of the equation $\tan \theta +\sec \theta =2\cos \theta$ and $\cos \theta \ne 0$  lying in the interval $\left(0,2\pi \right)$ is

If $6\cos 2\theta +2{\cos }^2\left(\frac{\theta }{2}\right)+2{\sin }^2\theta =0, -\pi <\theta <\pi ,$ then $\theta =$

The number of values of $x$ satisfying $\sin 4x=\cos 3x$ and $\frac{-\pi }{6}<x<\frac{\pi }{2},$ is