Answer to Question #144321 in Trigonometry for Shahir Sheikh

Question

cos^2(θ)tan^2(θ)

Answer 1

Recall that $\tan\theta=\frac{\sin\theta}{\cos\theta}$

$\cos^2\theta \tan^2\theta=\cos^2\theta.\left(\frac{\sin\theta}{\cos\theta}\right)^2\\ =\cos^2\theta.\frac{\sin^2\theta}{\cos^2\theta}=\sin^2\theta.$

Therefore, $\cos^2\theta \tan^2\theta=\sin^2\theta.$