Question

Verify sec^2x-tan^2x=(tanx)(cotx)?

Answer 1

`"see explanation"`

Explanation:

`"using the "color(blue)"trigonometric identities"`

`•color(white)(x)tanx=sinx/cosx" and "cotx=cosx/sinx`

`•color(white)(x)secx=1/cosx`

`"consider the left side"`

`1/cos^2x-sin^2x/cos^2x`

`=(1-sin^2x)/cos^2 x=cos^2x/cos^2x=1`

`"consider the right side"`

`sinx/cosx xxcosx/sinx=1`

`"left side "="right side "rArr"verified"`