Question

Prove esta identidade (tg²x + 1) x (sen²x - 1) = -1

Answer 1

$(tg^2x + 1) (sen^2x - 1) = \\ \\ (sec^2x)(-cos^2x) = \\ \\ \frac{1}{cos^2x}.(-cos^2x)= \\ \\ \frac{-cos^2x}{cos^2x}= -1 \ (cqd)$