SOLUTION: (csc^4 x )- (cot^4 x) states to factor and simplify

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Question 43447: (csc^4 x )- (cot^4 x) states to factor and simplify
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
cosec%5E4%28x%29+-+cot%5E4%28x%29
= %28cosec%28x%29%29%5E4+-+%28cot%28x%29%29%5E4
=
= %28cosec%5E2%28x%29+%2B+cot%5E2%28x%29%29%28cosec%5E2%28x%29+-+cot%5E2%28x%29%29
= %28cosec%5E2%28x%29+%2B+cot%5E2%28x%29%29%2A1 [since %28cosec%5E2%28x%29+-+cot%5E2%28x%29%29+=+1]
= 1%2Fsin%5E2%28x%29+%2B+cos%5E2%28x%29%2Fsin%5E2%28x%29
= %281+%2B+cos%5E2%28x%29%29%2Fsin%5E2%28x%29