If \frac{a+b}{\csc x}=\frac{a-b}{\cot x} show that \csc x \cot x=\frac{a^2-b^2}{4ab}

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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