SOLUTION: Show that (cosec^4x-1)/(cot^2x)=2+cot^2x

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Question 1140548: Show that (cosec^4x-1)/(cot^2x)=2+cot^2x
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
%28csc%5E4%28x%29-1%29%2F%28cot%5E2%28x%29%29=2%2Bcot%5E2%28x%29+
manipulating left side
=%28csc%5E4%28x%29-1%29%2F%28cot%5E2%28x%29%29.......use identity cot%5E2%28x%29=+csc%5E2%28x%29-1
=%28csc%5E4%28x%29-1%29%2F%28csc%5E2%28x%29-1%29.......factor numerator :
=%28+%28csc%5E2%28x%29-1%29+%28csc%5E2%28x%29%2B1%29%29%2F%28csc%5E2%28x%29-1%29......simplify
=
=csc%5E2%28x%29%2B1................use the following identity : csc+%5E2+%28x+%29=1%2B+cot+%5E2+%28x+%29
=1%2B+cot+%5E2+%28x+%29%2B1
=2%2B+cot+%5E2+%28x+%29