## Answers

Use power reduction formulas twice.

#### Explanation:

So,

and,

# = [color(blue)(1/2(1-cos6x))]^2#

# = 1/4[1-2cos6x+color(red)(cos^2 6x)]#

# = 1/4[1-2cos6x+(color(red)(1/2(1+cos12x)))]#

# = 1/8[2(1-2cos6x)+(1+cos12x))]#

# = 1/8[3-4cos6x+cos12x]#

The last expression can be integrated term by term using substitution for the two terms involving cosine.

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