4 pts Using a doubleangle or halfangle formula to simplify t

(4 pts) Using a double-angle or half-angle formula to simplify the given expressions | (a) If cos233°-sin233° n = cos Ao, then degrees -sin2 3r = cos B. then Note: You can earn partial credit on this problem

Solution

cos^2 33 - sin^ 2 33 = cos A

applying cos 2A formula

cos 2A = cos^2 A - sin^2 A

so we can write ,

cos^2 33 - sin^ 2 33 = cos (2* 33)

= cos 66

A = 66 degrees

b) cos^2 (3x ) - sin^2 (3x ) = cos B

cos^2 (3x ) - sin^2 (3x ) can be written as cos ( 2* 3x )

= cos (6x )

B = 6x