Question

已知cos(75°+α)=1/3,其中α是第三象限角,求cos(15°-α)+sin(a-15°)的值

Answer 1

α是第三象限角

cos(α+75°)>0

∴ α+75°是第四象限角

∵ cos(α+75°)=1/3

∴ sin(α+75°)=-√[1-cos²(α+75°)]=-√(1-1/9)=-2√2/3

∴ cos(15°-α)+sin(α-15°)

=cos(15°-α)-sin(15°-α)

=cos[90°-(75°+α)]-sin[90°-(75°+α)]

=sin(75°+α)-cos(75°+α)

=-2√2/3-1/3

=-(2√2+1)/3