Question

How do you prove `cos^2x(1-sec^2x)=-sin^2x`?

Answer 1

See Below

Explanation:

`LHS : cos^2x(1-sec^2x)`

`=cos^2x(-(sec^x-1))`->use the property`1+tan^2x=sec^2x`

`=cos^2x*(-tan^2x)`

`=cancel(cos^2x)*(-sin^2x)/cancel(cos^2x)`

`=-sin^2x`

`=RHS`