Question

已知a属于（3π/2，2π），化简根号1-sina 根号1 sina

Answer 1

√(2 2cosa)
=√(2 2(2cos^2(a/2)-1)
=√(4cos^2(a/2))
=-2cos(a/2)

1 sina cosa
=1 2sin(a/2)cos(a/2) 2cos^2(a/2)-1
=2cosa/2×(sina/2 cosa/2)

(1 sina cosa)(sina/2-cosa/2)/√(2 2cosa)
=[2cosa/2×(sina/2 cosa/2)](sina/2-cosa/2)/(-2cosa/2)
=-(sin^2a/2-cos^2a/2)
=cosa