Answer
$\displaystyle\int\frac{cosθ}{\sqrt {(1-sinθ)}}$ dx = =-2$\sqrt{(1-sinθ)}$ +c where c is an arbitrary constant
Work Step by Step
To solve this integral, we will attempt to find the derivative and antiderivative pair.
$\frac{d}{dx}(1-sinθ)^{\frac{1}{2}}$=$\frac{1}{2}(1-sinθ)^{-\frac{1}{2}}(-cosθ)$
=-$\frac{cosθ}{2\sqrt (1-sinθ)}$
Therefore, $\int\frac{cosθ}{\sqrt (1-sinθ)}$ dx = -2$\int-\frac{cosθ}{2\sqrt (1-sinθ)}$ dx
=-2$(1-sinθ)^{\frac{1}{2}}$ +c
=-2$\sqrt(1-sinθ)$ +c where c is an arbitrary constant
