Question

MEDAL + FAN

Answer 1

\[\tan^2\Theta*\cos^2\theta+\cos^2\theta=1\]

Answer 2

Rewrite the tan^2 in terms of sin^2 and cos^2.

Answer 3

what else i have 3 minutes to answer :( or i fail

Answer 4

\[\tan \Theta * \tan \Theta = \tan ^{2}\Theta \]\[\sin \Theta / \cos \Theta = \tan \Theta \] Substitute into the first equation.\[\sin \Theta / \cos \Theta *\sin \Theta /\cos \Theta = \sin ^2 \Theta /\cos ^{2}\] Substitute into the original equation.\[\sin ^{2}\Theta /\cos ^{2}\Theta * \cos ^{2}\Theta + \cos ^{2}\Theta = 1\] The cos^2 cancel out in the first term. And you get the Pythagorean identity \[\sin ^{2}\Theta + \cos ^{2}\Theta = 1\]