HELP! Honors Pre Calc homwork, verifying trig identities.
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Alright, so the first thing to do is find a least common denominator for your left side. It looks like it'll be sin(x)*(1-cos(x)). We'll have to multiply each numerator by the denominator of the other fraction, so this'll end up being sin^2(x) + (1-cos(x))^2, which, when expanded, is equal to sin^2(x) + cos^2(x) - 2cos(x) + 1. This, by the Pythagorean Identity, is equal to 1 - 2cos(x) + 1, or 2 - 2cos(x). We can factor this to 2(1-cos(x)). Thus, the "1-cos(x)" terms cancel in the top and bottom, and we are left with 2/sin(x), which is equal to 2csc(x) by the definition of cosecant, Q.E.D. Cheers!