Question 973695
{{{cos^4(x)-sin^4(x)+sin^2(x)}}}

First, you should be very familiar with 

{{{(a^2-b^2) = (a+b)(a-b)}}}


{{{((cos^2(x)+sin^2(x))(cos^2(x)-sin^2(x)))+(sin^2(x))}}} 

But recognize that the first to term add to 1. So 

{{{((cos^2(x)-sin^2(x)))+(sin^2(x))}}} 

and this reduces as well. to just 

{{{cos^2(x)}}}

Graphing software can be useful to check your answer to this type of problem.