If tan^2 theta = 2tan^2 phi + 1,then cos 2the | vedclass

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

Question

(B) Given: $	an^2 	heta = 2	an^2 \phi + 1$Adding $1$ to both sides: $1 + 	an^2 	heta = 2	an^2 \phi + 2$$\Rightarrow \sec^2 	heta = 2(1 + 	an^2

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(B) Given: $	an^2 	heta = 2	an^2 \phi + 1$Adding $1$ to both sides: $1 + 	an^2 	heta = 2	an^2 \phi + 2$$\Rightarrow \sec^2 	heta = 2(1 + 	an^2 \phi)$$\Rightarrow \sec^2 	heta = 2\sec^2 \phi$Taking the reciprocal: $\cos^2 	heta = \frac{1}{2} \cos^2 \phi$Using the identity $\cos^2 	heta = \frac{1 + \cos 2	heta}{2}$:$\frac{1 + \cos 2	heta}{2} = \frac{1}{2} \cos^2 \phi$$1 + \cos 2	heta = \cos^2 \phi$$1 + \cos 2	heta = 1 - \sin^2 \phi$$\cos 2	heta + \sin^2 \phi = 0$Alternatively,let $	heta = 45^\circ$. Then $	an^2 45^\circ = 2	an^2 \phi + 1 \Rightarrow 1 = 2	an^2 \phi + 1 \Rightarrow 	an^2 \phi = 0 \Rightarrow \phi = 0^\circ$.Thus,$\cos(2 	imes 45^\circ) + \sin^2 0^\circ = \cos 90^\circ + 0 = 0 + 0 = 0$.

If $\tan^2 \theta = 2\tan^2 \phi + 1$,then $\cos 2\theta + \sin^2 \phi$ equals

Similar Questions

The value of $\cos 12^\circ + \cos 84^\circ + \cos 156^\circ + \cos 132^\circ$ is

If $b \sin \alpha = a \sin (\alpha + 2\beta)$,then $\frac{a + b}{a - b} = $

If $\tan A = \frac{n}{n+1}$ and $\tan B = \frac{1}{2n+1}$,the value of $\tan (A+B) =$

If $x = \cos 10^\circ \cos 20^\circ \cos 40^\circ ,$ then the value of $x$ is

If $\sin A = n \sin B,$ then $\frac{n - 1}{n + 1} \tan \frac{A + B}{2} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module