16sin^4(11п/2-2а), если sin(3п/2-4а)=1/4

Question

16sin^4(11п/2-2а), если sin(3п/2-4а)=1/4

Answer 1

16sin^4(11π/2-2а) = 16* cos^4 (2α)

sin(3п/2-4а)= - cos (4α)= -(cos²(2α)-sin²(2α))= sin²(2α)-cis²(2α) = 1-cos²(2α)-cos²(2α) = 1-2cos²(2α) =1/4

1-2cos²(2α) =1/4
-2cos²(2α) =1/4-1
cos²(2α) =3/(4*2)
cos²(2α) =3/8

16* cos^4 (2α) =16* cos² (2α) *cos² (2α) = 16* 3/8 *3/8 = 9/4 =2,25

Ответ:2,25