sinx+cosx/sinx-cosx=2,则sin(x-5π)sin(3π/2-x)=?

题目

sinx+cosx/sinx-cosx=2,则sin(x-5π)sin(3π/2-x)=?

答案

(sinx+cosx)=2(sinx-cosx)
sinx=3cosx
又sin²x+cos²x=1
所以cos²x=1/10
sin(x-5π)sin(3π/2-x)=sin(x+π)(-cosx)
=sinxcosx
=3cos²x
=3/10