Write each expression without the square a 13sin22theta bcos

Write each expression without the square:

a. 1-3sin^2(2*theta)

b.cos^2(3*theta)

Solution (a)

Given

=> 1 - 3 sin^2 ()

use identity sin^2 () + cos^2 () = 1

=> sin^2 () + cos^2 () - 3 sin^2 ()

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

=> cos^2 () - 2 (1 - cos^2 ())

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

=> 2cos^2 () - 1 + cos^2 () - 1

use identity 2cos^() - 1 = cos (2)

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

sin^2 () = (1 cos 2())/2

=> cos (2) + (cos (2) - 1) /2

=> (3cos(2) - 1) /2

Solution:(b)

=> cos^2 (3)

multiply and divide by 2;

=> {2cos^2 (3)} / 2

=> {1 + 2cos^2 (3) - 1} / 2

use identity 2cos^() - 1 = cos (2)

=> {1 + cos (6)} /2