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

1 Answer
Apr 11, 2018

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