Practicing Success
The value of \(\frac{1}{cosecθ - cotθ}\) - \(\frac{1}{sinθ}\) is: |
tanθ cotθ sinθ cosecθ 1 |
cotθ |
\(\frac{1}{cosecθ - cotθ}\) - \(\frac{1}{sinθ}\) = \(\frac{sinθ}{1-cosθ}\) - \(\frac{1}{sinθ}\) = \(\frac{sin^2θ - 1 + cosθ}{sinθ (1-cosθ)}\) = \(\frac{cosθ (1-cos^2θ)}{sinθ (1-cosθ)}\) because sin2θ = 1-cos2θ = \(\frac{cosθ}{sinθ}\) (\(\frac{1-cos}{1-cosθ}\)) = cotθ |