若sin^4x+cos^4x=1,则sinθ+cosθ=?
问题描述:
若sin^4x+cos^4x=1,则sinθ+cosθ=?
答
sin^4x+cos^4x=(sin^2x+cos^2x)²-2sin^2xcos^2x=1-2sin^2xcos^2x=1∴2sin^2xcos^2x = 0sinxcosx =0(sinx+cosx)²= sin^2x+cos^2x+2sinxcosx=1+2sinxcosx=1∴sinx+cosx=1