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Verified answer
A)h'(x) = {(cos x - sin x)sin x - cos x(sin x + cos x)} / sin²x
= {sin x.cos x - sin²x - sin x.cos x - cos²x} / sin²x
= {-(sin²x + cos²x)} / sin²x
= {-1} / sin²x
= - 1/sin²x
h'(π/2) = h'(180/2) = h'(90)
= - 1/sin²90
= -1/1²
= -1