If theta is in the interval left(0, frac{pi}{ | vedclass

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

Question

(D) Given,$\cos 2 	heta \cdot \sec ^4 	heta + \sec ^2 	heta = 0$ for $	heta \in \left(0, \frac{\pi}{2}ight)$.Since $\sec 	heta 
eq 0$,we can d

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(D) Given,$\cos 2 	heta \cdot \sec ^4 	heta + \sec ^2 	heta = 0$ for $	heta \in \left(0, \frac{\pi}{2}ight)$.Since $\sec 	heta 
eq 0$,we can divide by $\sec ^2 	heta$:$\cos 2 	heta \cdot \sec ^2 	heta + 1 = 0$Using the identity $\cos 2 	heta = \frac{1 - 	an ^2 	heta}{1 + 	an ^2 	heta}$ and $\sec ^2 	heta = 1 + 	an ^2 	heta$:$\left(\frac{1 - 	an ^2 	heta}{1 + 	an ^2 	heta}ight) (1 + 	an ^2 	heta) + 1 = 0$$1 - 	an ^2 	heta + 1 = 0$$2 - 	an ^2 	heta = 0$$	an ^2 	heta = 2$Since $	an ^2 	heta = \frac{\sin ^2 	heta}{\cos ^2 	heta} = \frac{\sin ^2 	heta}{1 - \sin ^2 	heta} = 2$,we have:$\sin ^2 	heta = 2 - 2 \sin ^2 	heta$$3 \sin ^2 	heta = 2$$\sin ^2 	heta = \frac{2}{3}$

If $\theta$ is in the interval $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\cos 2 \theta \cdot \sec ^4 \theta + \sec ^2 \theta = 0$,then $\sin ^2 \theta =$

Similar Questions

If $e^{\sin x}-e^{-\sin x}-4=0,$ then the number of real values of $x$ is

The sum of the series $\sum_{n=1}^{\infty} \sin \left(\frac{n! \pi}{720}\right)$ is

$\tan 9^\circ - \tan 27^\circ - \tan 63^\circ + \tan 81^\circ = $

Evaluate: $\sqrt{\sin ^4 x+4 \cos ^2 x}-\sqrt{\cos ^4 x+4 \sin ^2 x}$

If $\text{cosec } A + \cot A = \frac{11}{2},$ then $\tan A = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module