函数F(X)=sin x+sin(x+π/2),x∈R 若f(x)=3/4,求sin2α的值

题目

函数F(X)=sin x+sin(x+π/2),x∈R 若f(x)=3/4,求sin2α的值

答案

F(X)=sin x+sin(x+π/2),
=sinx+cosx
=√2sin(x+π/4)
f(a)=3/4
sin(a+π/4)=sina+cosa=3√2/8
sin2a=2sinacosa=(sina+cosa)²-1=(3√2/8)²-1=9/32-1=-23/32