You need to know what the angle #theta# is.
For example, if #theta = 30^@#
The ratio of a #30^@-60^@-90^@# triangle is #1: sqrt(3): 2#
So #sin 30^@ = 1/2; sin^2 30^@ = (1/2)^2 = 1/4#
#cos 30^@ = sqrt(3)/2; cos^2 30^@ = (sqrt(3)/2)^2 = 3/4#
#tan 30^@ = 1/sqrt(3); tan^2 30^@ = (1/sqrt(3))^2 = 1/3#
Use the trigonometric double angle identities:
#cos 2 theta = cos^2 theta - sin ^2 theta#
#cos 2*30^@ = 3/4 - 1/4 = 2/4 = 1/2#
#tan 2 theta = (2 tan theta)/(1-tan^2 theta)#
#tan 2*30^@ = (2 *1/sqrt(3))/(1-1/3) = (2/sqrt(3))/(2/3) #
#= 2/sqrt(3) * 3/2 = 3/sqrt(3) * sqrt(3)/sqrt(3) = (3 sqrt(3))/3 = sqrt(3)#
