If a+bcsc⁡x=a−bcot⁡x show that csc⁡xcot⁡x=a2−b24ab

Walter Clyburn

Walter Clyburn

Answered question


If a+bcscx=abcotx show that cscxcotx=a2b24ab

Answer & Explanation



Beginner2022-01-15Added 42 answers

Suppose sinx0. Then we have that cscx=1sinx and cosxsinx=cotx
This implies in cosx=aba+b. Therefore, cscxcotx=cosxsin2x=cosx1cos2x
Notice that 1cos2x=1(aba+b)2=4ab(a+b)2
Then, cosx1cos2x=(ab)(a+b)4ab=a2b24ab

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