1)sin^2 (p+a)+sin^2 (3p/2+a); 2)(sin (p+a)-sin(3p/2-a))^2+(cos (2p-a)+cos (p/2-a))^2

Question

1)sin^2 (p+a)+sin^2 (3p/2+a); 2)(sin (p+a)-sin(3p/2-a))^2+(cos (2p-a)+cos (p/2-a))^2

Answer 1

1
sin²(π+a)+sin²(3π/2+a)=sin²a+cos²a=1
2
(sin(π+a)-sin(3π/2-a))²+(cos(2π-a)+cos(π/2-a))²=(-sina+cosa)²+(cosa+sina)²=
=sin²a-2sinacosa+cos²a+cos²a+2cosasina+sin²a=2(sin²a+cos²a)=2*1=2