cotx = (1 + cos2x)/(sin2x)
Note that, by the double-angle formulas for sine and cosine: i) cos(2x) = 2cos^2(x) - 1 ii) sin(2x) = 2sin(x)cos(x). So, we have: RHS = [1 + cos(2x)]/sin(2x) = [1 + 2cos^2(x) - 1]/[2sin(x)cos(x)], from the above identities = 2cos^2(x)/[2sin(x)cos(x)] = cos(x)/sin(x), by canceling 2cos(x) = cot(x) = RHS.
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