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

cos^2 x is the right answer.

Answer 2

`(\cos^2\O\cdot\tan^2\O)/(1-\cos^2\O)=(\cos^2\O\cdot\tan^2\O)/(\sin^2\O)=(\cos^2\O)/(\sin^2\O)\cdot\tan^2\O\\\\=(1)/((\sin^2\O)/(\cos^2\O))\cdot\tan^2\O=(1)/(\left((\sin\O)/(\cos\O)\right)^2)\cdot\tan^2\O=(1)/(\tan^2\O)\cdot\tan^2\O\\\\=(\tan^2\O)/(\tan^2\O)=1`


`Used:\\\\\sin^2\O+\cos^2\O=1\to1-\cos^2\O=\sin^2\O\\\\\tan\O=(\sin\O)/(\cos\O)`