Question

(1+ctg^2a)(cos^2a-1)
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Answer 1

ctg x = cos x / sin x

sin² x + cos² x = 1

(1 + ctg² a)(cos² a - 1) = (1 + cos² a / sin² a) * (-sin² a) = (sin² a + cos² a) / sin² a *(-sin² a) = 1  *(-1) = -1