note that for ANY fractions a/b and c/d, saying a/b = c/d is THE SAME as saying: ad = bc.

so let's "cross-multiply" to eliminate the "fractions":

a little algebra, now:

we have some terms that occur on both sides, so we can subtract them from each side:

(see it coming)? put the trig terms on one side, and the constant terms on the other:

.

now, to be really slick, write this proof "upside-down", starting with the basic trig identity, and ending with what you wanted to prove.