How do you verify the identity $2 + {cos}^{2} x - 3 {cos}^{4} x = {sin}^{2} x (3 + 2 {cos}^{2} x)$ $2+cos^2x-3cos^4x=sin^2x(3+2cos^2x)$ ?

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Answer 1 · 2017-01-17T18:59:00

see below

Left Hand Side;

$2 + {cos}^{2} x - 3 {cos}^{4} x = (1 - {cos}^{2} x) (2 + 3 {cos}^{2} x)$ $2+cos^2 x - 3 cos^4 x = (1-cos^2x)(2+3cos^2x)$ --> factors

use identity; ${sin}^{2} x + {cos}^{2} x = 1$ $sin^2 x + cos ^2 x =1$

$= {sin}^{2} x (2 + 3 {cos}^{2} x)$ $=sin^2 x (2+3 cos ^2 x)$

$:.=$ Right Hand Side

How do you verify the identity 2+cos^2x-3cos^4x=sin^2x(3+2cos^2x)2+cos2x−3cos4x=sin2x(3+2cos2x)2+cos^2x-3cos^4x=sin^2x(3+2cos^2x)?