Test Index

UPSC NDA I and II 2020 Math Solved Paper

© examsnet.com

Question : 8 of 120

Marks: +1, -0

If

tan\theta =\frac{cos17^{∘}-sin17^{∘}}{cos17^{∘}+sin17^{∘}},

then what is the value of θ?

0°
28°
38°
52°

Solution:

Concept:

Use the formula

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

and the known value

\tan 45^\circ = 1

.

Explanation:

Given

\tan\theta = \frac{\cos 17^\circ - \sin 17^\circ}{\cos 17^\circ + \sin 17^\circ}

.

Divide numerator and denominator by

\cos 17^\circ

:

\frac{\frac{\cos 17^\circ}{\cos 17^\circ} - \frac{\sin 17^\circ}{\cos 17^\circ}}{\frac{\cos 17^\circ}{\cos 17^\circ} + \frac{\sin 17^\circ}{\cos 17^\circ}} = \frac{1 - \tan 17^\circ}{1 + \tan 17^\circ}

.

Rewrite using

\tan 45^\circ = 1

:

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

.

This matches the identity for

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

.

Thus,

\tan\theta = \tan(28^\circ)

.

Since

\theta

is an acute angle, we have

\theta = 28^\circ

.

Answer:

Option B:

28^\circ

(option 2 in the given list).

© examsnet.com

Go to Question:

Prev Question

Next Question