Using a double-angle or half-angle formula to simplify the given expressions.

Question

(a) If cos 2 ( 22 ∘ ) − sin 2 ( 22 ∘ ) = cos ( A ∘ ), then

A=________ degrees.

(b) If cos2(4x)−sin2(4x)=cos(B),cos2(4x)-sin2(4x)=cos(B), then

B=___________

Answer 1

cos²θ - sin²θ = cos(2θ)

So, cos²22º - sin²22º = cos44º and cos²(4x) - sin²(4x) = cos(8x).

Answer 2

cos^2(22)-sin^22=cos(A)

.8596 -.3746 = " "

.485= " "

A=60.6833.........

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

You need to substitute.

B=___________