Question

How do you verify sin^2tan^2=tan^2-sin^2?

Answer 1

we will start with tan^2 theta - sin^2 theta

`\tan ^2\text{ }\theta-sin^2\theta`

remember tan theta = sin theta / cos theta

`((\sin \theta)/(\cos \theta))^2\text{ - }\sin ^2\theta`
`((\sin\theta)/(\cos\theta))^2\text{ - }\sin ^2\theta\text{ }\ast(\cos ^2\theta)/(\cos ^2\theta)`
`(\sin ^2\theta(1-\cos ^2\theta))/(\cos ^2\theta)`
`\tan ^2\theta\text{ (1 - }\cos ^2\theta\text{)}`
`\tan ^2\theta\ast\sin ^2\theta`