use the double angle formula to rewrite.

Question

6cos^2-3

and

(cosx +sinx)(cosx-sinx)

Answer 1

cos ( 2 x ) = 2 cos ^ 2 ( x ) - 1

6 cos ^ 2 ( x ) - 3 =

3 [ 2 cos ^ 2 ( x ) - 1 ] =

3 sin ( 2 x )

Answer 2

second one:

(cosx +sinx)(cosx-sinx)
=(cosx +sinx)(cosx-sinx) * (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