Question

show that questions in diagrams

Answer 1

Here we will start from RHS and reach the LHS.

RHS=

$1 - 2 \cos^{2} x \\ = 1 - 2 \cos ^{2} x + \cos ^{4} x - \cos ^{4} x \\ = \cos ^{4} x - 2 \cos ^{2} x + 1 - \cos ^{4} x \\ = {(1 - \cos ^{2}x )}^{2} - \cos ^{4} x \\ = \sin ^{4}x - \cos ^{4} x$

= LHS

(Identities used sin^2(x)+cos^2(x)=1, (a-b)^2=a^2-2ab+b^2)