Question

How do you verify `tan^2x-tan^2x*sin^2x=sin^2x`?

Answer 1

Please see below.

Explanation:

`tan^2x-tan^2x*sin^2x`

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

= `tan^2xcos^2x`

= `sin^2x/cos^2x*cos^2x`

= `sin^2x`

Answer 2

`"see explanation"`

Explanation:

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

`•color(white)(x)tanx=sinx/cosx`

`•color(white)(x)sin^2x+cos^2x=1`

`"consider the left side"`

`"take out a common factor "tan^2x`

`tan^2x(1-sin^2x)`

`=sin^2x/cancel(cos^2x)xxcancel(cos^2x)`

`=sin^2x=" right side "rArr"verified"`