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View Full Version : How to solve cot^2x - csc^2x?


mollie2539
Dec 4, 2010, 07:57 PM
Please solve cot^2x - csc^2x =

depree
Dec 4, 2010, 08:35 PM
cot(x) is defined as adjacent / opposite.
csc(x) is defined as hypotenuse / opposite
So csc^2(x) - cot^2(x) = (hyp^2 - adj^2) / opp^2.
By the pythagorean theorem, (hyp^2 - adj^2) = opp^2
therefore, csc^2(x) - cot^2(x) = 1
Therefore, -csc^2(x) + cot^2(x) = -1
Q.E.D.