SOLUTION: I don't get how to verify trig identities such as: {{{cot^2y(sec^2y-1)= 1}}}. How is this done?

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Question 132844: I don't get how to verify trig identities such as: cot%5E2y%28sec%5E2y-1%29=+1. How is this done?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm only manipulating the left side. I'm only showing the right side for comparison.

cot%5E2y%28sec%5E2y-1%29=+1 Start with the given equation


cot%5E2y%28%28tan%28y%29%29%5E2%29=+1 Replace sec%5E2y-1 with %28tan%28y%29%29%5E2


%281%2F%28%28tan%28y%29%29%5E2%29%29%28%28tan%28y%29%29%5E2%29=+1 Replace cot%5E2y with 1%2F%28%28tan%28y%29%29%5E2%29


%28%28tan%28y%29%29%5E2%29%2F%28%28tan%28y%29%29%5E2%29=+1 Multiply


1+=+1 Divide and cancel like terms. Since the two sides are equal, this verifies the identity.