If A + B + C = pi , then cos , 2A + cos , 2B | vedclass

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

Question

(C) Given $A + B + C = \pi$,so $A + B = \pi - C$. $L.H.S. = \cos 2A + \cos 2B + \cos 2C$ $= 2 \cos (A + B) \cos (A - B) + (2 \cos^2 C - 1)$ $= 2 \cos

Vedclass · Accepted Answer

$- 1 - 4 \cos A \cos B \cos C$

Vedclass · Answer

(C) Given $A + B + C = \pi$,so $A + B = \pi - C$. $L.H.S. = \cos 2A + \cos 2B + \cos 2C$ $= 2 \cos (A + B) \cos (A - B) + (2 \cos^2 C - 1)$ $= 2 \cos (\pi - C) \cos (A - B) + 2 \cos^2 C - 1$ $= - 2 \cos C \cos (A - B) + 2 \cos^2 C - 1$ $= - 1 - 2 \cos C [\cos (A - B) - \cos C]$ Since $C = \pi - (A + B)$,$\cos C = - \cos (A + B)$. $= - 1 - 2 \cos C [\cos (A - B) + \cos (A + B)]$ $= - 1 - 2 \cos C [2 \cos A \cos B]$ $= - 1 - 4 \cos A \cos B \cos C$.

If $A + B + C = \pi ,$ then $\cos \, 2A + \cos \, 2B + \cos \, 2C = $

Similar Questions

If $A = \cos^2 \theta + \sin^4 \theta$,then for all values of $\theta$:

The maximum value of $3\cos \theta - 4\sin \theta$ is

If $A + B + C = \pi$ and $\sin \left( A + \frac{C}{2} \right) = k \sin \frac{C}{2}$,then $\tan \frac{A}{2} \tan \frac{B}{2} = $

If $A+B+C=\pi$,then $\sin A-\sin B+\sin C=$

Prove that $\cos ^{2} x+\cos ^{2}\left(x+\frac{\pi}{3}\right)+\cos ^{2}\left(x-\frac{\pi}{3}\right)=\frac{3}{2}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module