Question

Simplify each of the following using the trig identities. `(sin^2x)+(sin^2x)(tan^2x)`?

Answer 1

`sin^2x+sin^2xtan^2x=tan^2x`

Explanation:

Simplify: `sin^2x+sin^2xtan^2x`

First, factor out `sin^2x` from the expression:

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

Now we can use this trig identity

`1+tan^2x=sec^2x`

Now we have

`sin^2xsec^2x`

We know that

`secx=1/cosx`

So it is then true that

`sec^2x=1/cos^2x`

Now we have

`sin^2x/cos^2x`

We know that

`tanx=sinx/cosx`

So it is then true that

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

So for the final answer we have is

`tan^2x`