Using a double-angle or half-angle formula to simplify the given expressions. If cos ^2 ( 2 x ) − sin ^2 ( 2 x ) = cos ( B ) , then B =

Answer 1

The double-angle formula for cosine is:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

if a = b, then:

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

To get the two terms on the right to be functions of 2x, let a = 2x, then 2a = 4x and:

cos(4x) = cos^2(2x) - sin^2(2x) = cos(B)

Thus, cos(B) = cos(4x) implies B = 4x