# Thread: Need help with simple trig proof

1. ## Need help with simple trig proof

Use the Pythagorean Trig Identity, sin^2θ+cos^2θ=1, to prove that sin^4θ-cos^4θ=1-2cos^2θ.

With the advice of my teacher, I started by making a chart. One side is "sin^4θ - cos^4θ", and the other is "1 - 2cos^2θ". He said I'm not supposed to plug in any numerical values, but I'm not sure what to do next.

2. ## Re: Need help with simple trig proof

$\sin^4(\theta) - \cos^4(\theta) =$

$(\sin^2(\theta)-\cos^2(\theta))(\sin^2(\theta)+\cos^2(\theta)) =$

$\sin^2(\theta)- \cos^2(\theta) =$

$(1-\cos^2(\theta))-\cos^2(\theta) =$

$1 - 2\cos^2(\theta)$