Question

Using sin^2x+ cos^2 x=1 and other trig properties, simplify the following: (cos^2Ø*tan^2Ø)/(1-cos^2 Ø.

Answer 1

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

$Used:\\\\\sin^2\O+\cos^2\O=1\to1-\cos^2\O=\sin^2\O\\\\\tan\O=\dfrac{\sin\O}{\cos\O}$

Answer 2

cos^2 x is the right answer.