Question

sin^4Q-cos=1-2cos^2Q​

Answer 1

sin^2+cos^2=1———————-(1)

cos^2=1-sin^2———————-(2)

lhs=sin^2+cos^4

=sin^2+cos^2(cos^2)

=sin^2+cos^2(1-sin^2)———————from(2)

=sin^2+cos ^2-(cos^2)(sin^2)

=1-(1-sin^2)sin^2—————————from(2)

=1-sin^2+sin^4

=cos^2+sin^4——————————-from(2)

=rhs

hence proved.

Hope helps

Answer 2

Answer:

Step-by-step explanation:

sin^4Q-cos^4Q=1-2cos^2Q​

LHS=sin^4Q-cos^4Q

(sin^2Q+cos^2Q)(sin^2Q-cos^2Q)

=sin^2Q-cos^2Q

=1-cos^2Q-cos^2Q

=1-2-cos^2Q=RHS

Proved