Question

find the value of cos^4 A − sin^4

Answer 1

cos^4 a - sin^4 a = cos2a

Let us rewrite:

(cos^2 a)^2 - (sin^2 a)^2

We know that:

a^2 - b^2 = (a-b)(a+b)

==> cos^4 a- sin^4 a=(cos^2 a - sin^2 a)(cos^2 a + sin^2 a)

Also:

We know that:

cos^2 a-sin^2 a = cos2a

cos^2 a + sin^2 a= 1

Now substitute:

cos^4 a - sin^4 a= cos2a * 1

                              = cos2a