I f θ + θ = {2} (90 - θ), then cot θis

Correct Answer is : 2−1{2} - 12−1

Correct Answer is : 2−1{2} - 12−1

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RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

Question : 6 of 120

Marks: +1, -0

I f

\sin \theta + \cos \theta = \sqrt{2} \cos(90 - \theta)

, then cot θis

Solution:

Concept:

Use

\cos(90^\circ-\theta)=\sin\theta

to simplify the given equation.

Explanation:

Given:

\sin\theta+\cos\theta=\sqrt{2}\cos(90^\circ-\theta)

Since

\cos(90^\circ-\theta)=\sin\theta

, we get:

\sin\theta+\cos\theta=\sqrt{2}\sin\theta

Rearrange the terms:

\cos\theta=\sqrt{2}\sin\theta-\sin\theta

\cos\theta=(\sqrt{2}-1)\sin\theta

Divide both sides by

\sin\theta

\cot\theta=\sqrt{2}-1

This is the required value.

Answer:

\cot\theta=\sqrt{2}-1

, so option D is correct.

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