How do you simplify #\frac{\sin^4 \theta - \cos^4 \theta}{\sin^2 \theta - \cos^2 \theta} # using the trigonometric identities?

1 Answer
Gió
Dec 22, 2014

You should get: #(sin^4(theta)-cos^4(theta))/(sin^2(theta)-cos^2(theta))=1#

This is because in the numerator you have:

#sin^4(theta)-cos^4(theta)# which is the same as:

#[sin^2(theta)+cos^2(theta)]*[sin^2(theta)-cos^2(theta)]#

(Remember that #(a+b)*(a-b)=a^2-b^2#)

So your fraction becomes:

#([sin^2(theta)+cos^2(theta)]*[sin^2(theta)-cos^2(theta)])/(sin^2(theta)-cos^2(theta))=#

You can now simplyfy the two: #sin^2(theta)-cos^2(theta)# in the numerator and denominator.
You are left with:
#[sin^2(theta)+cos^2(theta)]# which is always equal to 1 (for every angle #theta#)

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