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RRB Group D 27 Nov 2025 Shift 3 Solved Paper

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Question : 47 of 100

Marks: +1, -0

If

cos\theta =\frac{5}{13}

, then find the value of

\sqrt{\frac{1-sin\theta }{1+sin\theta }}

.

$\frac{1}{25}$
$\frac{1}{3}$
$\frac{12}{13}$
$\frac{1}{5}$

Solution:

Concept:

Use the Pythagorean identity to find

\sin\theta

, then simplify the given expression.

Explanation:

Start with

\cos\theta = \frac{5}{13}

.

Use

\sin^2\theta + \cos^2\theta = 1

.

So

\sin^2\theta = 1 - \cos^2\theta = 1 - \left(\frac{5}{13}\right)^2 = 1 - \frac{25}{169} = \frac{144}{169}

.

Thus

\sin\theta = \frac{12}{13}

(positive, since angle likely acute).

Now substitute into

\sqrt{\frac{1-\sin\theta}{1+\sin\theta}}

:

\sqrt{\frac{1-\frac{12}{13}}{1+\frac{12}{13}}} = \sqrt{\frac{\frac{1}{13}}{\frac{25}{13}}} = \sqrt{\frac{1}{25}} = \frac{1}{5}

.

Answer:

\frac{1}{5}

(Option D).

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