First slide

Diffrentiation

Question

Differentiate the following with respect to $θ .$
$\frac{\cos θ}{(1 - \sin θ)}$

Moderate

A

$\frac{1}{1 + 2 \sin θ}$
B

$\frac{1}{1 + \sin θ}$
C

$\frac{1}{1 - 2 \sin θ}$
D

$\frac{1}{1 - \sin θ}$

Solution

$\begin{array}{l} y^{'} = \frac{- \sin θ (1 - \sin θ) + \cos θ (\cos θ)}{(1 - \sin θ)^{2}} \\ = \frac{- \sin θ + \sin^{2} θ + \cos^{2} θ}{(1 - \sin θ)^{2}} \\ = \frac{1 - \sin θ}{(1 - \sin θ)^{2}} = \frac{1}{1 - \sin θ} \end{array}$

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