The general value of theta satisfying the equ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given equation: $	an^2 	heta + \sec 2	heta = 1$.Using the identity $\sec 2	heta = \frac{1 + 	an^2 	heta}{1 - 	an^2 	heta}$,the equation be

Vedclass · Accepted Answer

$m\pi, n\pi \pm \frac{\pi}{3}$

Vedclass · Answer

(B) Given equation: $	an^2 	heta + \sec 2	heta = 1$.Using the identity $\sec 2	heta = \frac{1 + 	an^2 	heta}{1 - 	an^2 	heta}$,the equation becomes:$	an^2 	heta + \frac{1 + 	an^2 	heta}{1 - 	an^2 	heta} = 1$.Let $x = 	an^2 	heta$. Then $x + \frac{1+x}{1-x} = 1$.$x(1-x) + 1 + x = 1 - x$$x - x^2 + 1 + x = 1 - x$$3x - x^2 = 0 \Rightarrow x(3 - x) = 0$.So,$	an^2 	heta = 0$ or $	an^2 	heta = 3$.If $	an^2 	heta = 0$,then $	an 	heta = 0 \Rightarrow 	heta = m\pi$ for any integer $m$.If $	an^2 	heta = 3$,then $	an 	heta = \pm \sqrt{3} \Rightarrow 	heta = n\pi \pm \frac{\pi}{3}$ for any integer $n$.Thus,the general solution is $	heta = m\pi, n\pi \pm \frac{\pi}{3}$.

The general value of $\theta$ satisfying the equation $\tan^2 \theta + \sec 2\theta = 1$ is

Similar Questions

If $\cos \theta + \cos 2\theta + \cos 3\theta = 0$,then the general value of $\theta$ is

The solution set of the equation $\tan(\pi \tan x) = \cot(\pi \cot x)$ is

Solve $\cos x = \frac{1}{2}$

The general solution of the trigonometric equation $(\sqrt{3}-1) \sin \theta + (\sqrt{3}+1) \cos \theta = 2$ is

The number of possible solutions of $\sin \theta + \sin 4 \theta + \sin 7 \theta = 0$ for $\theta \in (0, \pi)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module