Question

cos^2a(1+tg^2a)-sin^2a=cos^2a докажите тождество

Answer 1

$\cos^2 \alpha \cdot (1+\tan^2 \alpha )-\sin^2 \alpha =\cos^2 \alpha +\cos^2 \alpha \cdot \dfrac{\sin^2 \alpha }{\cos^2 \alpha } -\sin^2 \alpha =\\\\=\cos^2 \alpha +\sin^2 \alpha -\sin^2 \alpha =\cos^2 \alpha$