Question

Mostre que: (1-tan²α) (1- sin²α) = 1-2sin²α

Answer 1

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