Trigonometry
posted by Josh G. .
use the double angle formula to rewrite.
6cos^23
and
(cosx +sinx)(cosxsinx)

cos ( 2 x ) = 2 cos ^ 2 ( x )  1
6 cos ^ 2 ( x )  3 =
3 [ 2 cos ^ 2 ( x )  1 ] =
3 sin ( 2 x ) 
second one:
(cosx +sinx)(cosxsinx)
=(cosx +sinx)(cosxsinx) * (cosx + sinx)/(cosx + sinx)
= (cos^2 x + 2sinxcosx + sin^2 x)/(cos^2 x  sin^2 x)
= (1 + sin 2x)/cos 2x
or
1/cos 2x + sin 2x/cos 2x
= sec 2x + tan 2x