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UPSC NDA II 2024 Mathematics Paper

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Question : 30 of 120

Marks: +1, -0

What is

\rm \frac{\cos 17^\circ-\sin 17^\circ}{\cos 17^\circ+\sin 17^\circ}

equal to

tan 34°
cot 34°
tan 62°
cot 62°

Solution:

Concept:

Simplify the given expression using

\tan\theta

and the tangent subtraction formula.

Explanation:

Step 1: Divide numerator and denominator by

\cos 17^\circ

.

This gives

\frac{1-\tan 17^\circ}{1+\tan 17^\circ}

.

Step 2: Use

\tan 45^\circ = 1

to rewrite the expression as

\frac{\tan 45^\circ - \tan 17^\circ}{1 + \tan 45^\circ \tan 17^\circ}

.

Step 3: Apply the identity

\tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}

.

Here

A=45^\circ

and

B=17^\circ

, so the expression equals

\tan(45^\circ - 17^\circ) = \tan 28^\circ

.

Step 4: Use the complementary angle identity:

\tan\theta = \cot(90^\circ - \theta)

.

Thus

\tan 28^\circ = \cot(90^\circ - 28^\circ) = \cot 62^\circ

.

Answer:

\cot 62^\circ

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