prove that cos^4A - cos^2A = sin^4A - sin^2A - Maths - Introduction to Trigonometry

Question

prove that cos^4A - cos^2A = sin^4A - sin^2A

Varun.Rawat · Accepted Answer

$L H S = \cos^{4} A - \cos^{2} A = \cos^{2} A [\cos^{2} A - 1] = - \cos^{2} A [1 - \cos^{2} A] = - \cos^{2} A \sin^{2} A = - \sin^{2} A [1 - \sin^{2} A]$ $= \sin^{4} A - \sin^{2} A = R H S$

prove that . cos^4A - cos^2A = sin^4A - sin^2A