First slide

Trigonometric Identities

Question

If $\frac{π}{2} < θ < π$ , then $\sqrt{\frac{1 - \sin θ}{1 + \sin θ}} + \sqrt{\frac{1 + \sin θ}{1 - \sin θ}}$ is equal to is

Moderate

A

$2 \sec θ$
B

$- 2 \sec θ$
C

$s e c θ$
D

$- s e c θ$

Solution

We have,
$\begin{array}{l} \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} + \sqrt{\frac{1 + \sin θ}{1 - \sin θ}} \\ = \frac{1 - \sin θ + 1 + \sin θ}{\sqrt{1 - \sin^{2} θ}} \\ = \frac{2}{| \cos θ |} = \frac{2}{- \cos θ} = - 2 \sec θ, [\begin{array}{l} ∵ π / 2 < θ < π \\ ∴ \cos θ < 0 \end{array}] \end{array}$

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