If a tan theta = b,then a cos 2theta + b sin | vedclass

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

Question

(A) Given that $	an 	heta = \frac{b}{a}$.Now,$a \cos 2	heta + b \sin 2	heta = a \left( \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta} ight) + b \le

Vedclass · Accepted Answer

$a$

Vedclass · Answer

(A) Given that $	an 	heta = \frac{b}{a}$.Now,$a \cos 2	heta + b \sin 2	heta = a \left( \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta} ight) + b \left( \frac{2 	an 	heta}{1 + 	an^2 	heta} ight)$.Substituting $	an 	heta = \frac{b}{a}$,we get:$= a \left( \frac{1 - \frac{b^2}{a^2}}{1 + \frac{b^2}{a^2}} ight) + b \left( \frac{2 \frac{b}{a}}{1 + \frac{b^2}{a^2}} ight)$$= a \left( \frac{a^2 - b^2}{a^2 + b^2} ight) + b \left( \frac{2ab}{a^2 + b^2} ight)$$= \frac{a^3 - ab^2 + 2ab^2}{a^2 + b^2}$$= \frac{a^3 + ab^2}{a^2 + b^2} = \frac{a(a^2 + b^2)}{a^2 + b^2} = a$.

If $a \tan \theta = b$,then $a \cos 2\theta + b \sin 2\theta = $

Similar Questions

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

$\tan 20^\circ \cot 10^\circ \cot 50^\circ$ is equal to

What is the value of $\cos \left(22 \frac{1}{2}\right)^{\circ}$?

If $\tan \theta = t,$ then $\tan 2\theta + \sec 2\theta = $

If $p = \tan 20^{\circ}$,then the value of $\frac{\tan 160^{\circ} - \tan 110^{\circ}}{1 + \tan 160^{\circ} \tan 110^{\circ}}$ in terms of $p$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module