Question

WILL FAN AND MEDAL

1+cos(12x)=?
A.2cos^2(12x)
B.2sin^2(12x)
C.2cos^2(6x)
D.2sin^2(6x)

Answer 1

Here's a really good list of trig identities
http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf
http://www.sosmath.com/trig/Trig5/trig5/trig5.html

Answer 2

hmm we have \(\cos(12x)=\cos(2(6x))=\cos^26x-\sin^26x\)
then \(1+\cos(12x)=1+\cos^26x-\sin^26x=2\cos^26x\)

Answer 3

the identity i used is \(\cos2x=\cos^2x-\sin^2x\)

Answer 4

Awesome job @xapproachesinfinity

Answer 5

Another way is to see that \[\Large \frac{ 1+\cos(2x) }{ 2 }=\cos^2x\]

Answer 6

You're only left with C because \[\Large \frac{1-\cos(2x)}{2}=\sin^2x\] and there is no subtraction sign.

Anyway, just to be sure set C equal to 1+cos(12x)
\[\Large 1+\cos(12x)=2\cos^2(6x)\]

Divide both sides by two
\[\Large \frac{1+\cos(12x)}{2}=\cos^2(6x)\]

And you're left with your identitity