Prove the following identity:
$cotθ minus tanθ space equals space fraction numerator 2 space cos squared straight theta minus 1 over denominator sinθ minus cosθ end fraction.$

Name: Wired Faculty - The Best Learning App
Rating: 4.6 (1864 reviews)

Solution

cot space straight theta space minus space tanθ space equals space fraction numerator 2 space cos squared straight theta minus 1 over denominator sinθ. space cosθ end fraction

L.H.S. =

cot space straight theta space minus space tanθ

equals space cosθ over sinθ minus sinθ over cosθ equals fraction numerator cos squared straight theta minus sin squared straight theta over denominator sinθ. space cosθ end fraction equals space fraction numerator cos squared straight theta minus left parenthesis 1 minus cos squared straight theta right parenthesis over denominator sinθ. space cosθ end fraction space equals space fraction numerator cos squared straight theta minus 1 plus cos squared straight theta over denominator sinθ. space cosθ end fraction equals space fraction numerator 2 space cos squared straight theta minus 1 over denominator sinθ. space cosθ end fraction space equals space straight R. straight H. straight S.

Hence, L.H.S. = R.H.S.

For Daily Free Study Material Join wiredfaculty