Use the fundamental identities to fully simplify the expression. tanx sinx+ secx cos^2x. Explain how you do it

First, remember that:

and:

Then we can rewrite the expression:

Where A is an equivalent expression.

as:

Then this is:

Now we can multiply both sides by cos(x), then:

And we know that the left term of the above equation is equal to 1, then:

And A is equivalent to the original expression, then we get:

The simplification of the expression is sec(x)

yes.. it's proven to be 36.