Hello, KevinShaughnessy!
What they did was correct.
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Hi,
Does the answer key section here for number 2 makes sense? It seems like they went from cos^2 - sin^2 to cos^2 + sin^2 for no reason.
http://i.imgur.com/bdyQPrJ.png
Thanks.
Yes, the answer key is perfectly correct. The problem is to prove the trig identity . They do that by using the "double angle" identities: and to write the left side as .
Of course we can cancel the "sin(t)" terms in the first fraction to get
and turn the first "2cos(t)" into a fraction by multiplying both numerator and denominator by cos(t):
.
Now add the fractions, remembering to distribute that "-" in front of the second fraction:
.