#(sin 60^o)^2 + (cos 60^o)^2 = 1#
In fact, for any angle #theta# we have #sin^2theta + cos^2theta = 1#
We can see this geometrically for positive angles less than #90^o# (e.g. #60^o#) by considering a right angled triangle with angles #theta#, #90^o - theta# and #90^o# and hypotenuse of length #1#.
By the definitions of #sin theta# and #cos theta#, the side opposite the angle #theta# will be of length #sin theta# and the side adjacent to the angle #theta#, opposite the #90^o - theta# angle will be of length #cos theta#.
