verify the identity
sinx cosx+sinx/cosx+cos^2x=tanx

Please verify that your equation is the following:

\frac{sin(x)cos(x) + sin(x)}{cos(x) + cos^2(x)} = tan(x)

If so, the answer depends on factoring the top half and the bottom half of the fraction side of the equation and on a quotient identity.

First, factor the top portion of the fraction:
\frac{sin(x)(cos(x) + 1)}{cos(x) + cos^2(x)} = tan(x)

Second, factor the bottom portion of the fraction:
\frac{sin(x)(cos(x) + 1)}{cos(x)(1 + cos(x))} = tan(x)

Now you can see how the top and bottom partially cancel:
\frac{sin(x)(cos(x) + 1)}{cos(x)(1 + cos(x))} = \frac{sin(x)}{cos(x)} * \frac{1 + cos(x)}{1 + cos(x)} = \frac{sin(x)}{cos(x)} * 1 = \frac{sin(x)}{cos(x)}

The quotient identity verifies that sin/cos=tan through right angle trig...

Good luck, and if something is not clear please post back with any questions.

It is AMHD policy not to do homework - Ask Me Help Desk - Announcements in Forum : Homework Help