Question

How do you prove `sec^2x-tan^2x =cos^2x+sin^2x`?

Answer 1

See below

Explanation:

Using:
`1+sec^2x=tan^2x`
`1=sin^2x+cos^2x`

Start:
`sec^2x-tan^2x =cos^2x+sin^2x`

`(1+tan^2x)-tan^2x=cos^2x+sin^2x`

`1+cancel(tan^2x)cancel(-tan^2x)=cos^2x+sin^2x`

`1=cos^2x+sin^2x`

`cos^2x+sin^2x=cos^2x+sin^2x`