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.

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- Jun 29th 2013, 03:35 PMKevinShaughnessy[Trig Proof] Does this answer key make sense?
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. - Jun 29th 2013, 04:47 PMSorobanRe: [Trig Proof] Does this answer key make sense?
Hello, KevinShaughnessy!

What they did was correct.

Quote:

n . . . . . . . . .

n . . . . . . . . .

n . . . . . . . . .

n . . . . . . . . .

n . . . . . . . . .

n . . . . . . . . . - Jun 29th 2013, 04:49 PMHallsofIvyRe: [Trig Proof] Does this answer key make sense?
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:

. - Jun 30th 2013, 03:13 PMKevinShaughnessyRe: [Trig Proof] Does this answer key make sense?
Thanks guys, looks like I need a bit of work on knowing when to distribute a negative.