# Please help me simplify. What is #cos^4theta -sin^4theta +sin^2theta# equal to?

##### 2 Answers

May 31, 2018

#### Explanation:

We have

Now we use that

So we get

May 31, 2018

#### Explanation:

#cos^4theta-sin^4theta" is a "color(blue)"difference of squares"#

#â€¢color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=cos^2theta" and "b=sin^2theta#

#cos^4theta-sin^4theta=(cos^2theta-sin^2theta)(cos^2theta+sin^2theta)#

#[cos^2theta+sin^2theta=1]#

#cos^4theta-sin^4theta+sin^2theta#

#=cos^2theta-sin^2theta+sin^2theta#

#=cos^2theta#