SOLUTION: Verify the identity {{{ (csc^4(x)-1)/(cot^2(x)) = 2 + cot^2(x) }}}

Algebra ->  Trigonometry-basics -> SOLUTION: Verify the identity {{{ (csc^4(x)-1)/(cot^2(x)) = 2 + cot^2(x) }}}      Log On


   

Question 1131256: Verify the identity
+%28csc%5E4%28x%29-1%29%2F%28cot%5E2%28x%29%29+=+2+%2B+cot%5E2%28x%29+
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Verify the identity
+%28csc%5E4%28x%29-1%29%2F%28cot%5E2%28x%29%29+=+2+%2B+cot%5E2%28x%29+
+csc%5E4%28x%29-1+=+2cot%5E2%28x%29+%2B+cot%5E4%28x%29+
1+-+sin%5E4%28x%29+=+2sin%5E2%28x%29cos%5E2%28x%29+%2B+cos%5E4%28x%29
1+=+sin%5E4%28x%29+%2B+2sin%5E2%28x%29cos%5E2%28x%29+%2B+cos%5E4%28x%29
1+=+%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29%5E2
1 = 1^2
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I'm still waiting for an example where working only one side makes a difference.