# Thread: Solving Trig Idenities PLZ NEED HELP

1. ## Solving Trig Idenities PLZ NEED HELP

Hi there I need help with this question! It says to factor out the left side of the equation but I don't see how it works. Can someone please leave me a step by step guide? Thank you!!!!

Question:

cos4x + 2cos2xsin2x + sin4x = 1

2. Originally Posted by Sarah32
Hi there I need help with this question! It says to factor out the left side of the equation but I don't see how it works. Can someone please leave me a step by step guide? Thank you!!!!

Question:

cos4x + 2cos2xsin2x + sin4x = 1
I presume this is
$\displaystyle cos^4(x) + 2cos^2(x)sin^2(x) + sin^4(x) = 1$

Note that the LHS is a perfect square. If your teacher gave you the factoring problem
$\displaystyle x^4 + 2x^2 y^2 + y^4$
you would probably see more easily that this is
$\displaystyle = (x^2 + y^2)^2$

So your equation becomes
$\displaystyle (cos^2(x) + sin^2(x))^2 = 1$

-Dan

### 2cos2xsin2x

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