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UPSC NDA Math Model Paper 4

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Question : 43 of 120

Marks: +1, -0

Find the maximum value of

|2 - \sin\theta|

.

3
2
1
-1

Solution:

Using the definition of modulus function, we have the following two cases:

CASE 1: If

2 - \sin\theta \ge 0 \Rightarrow 2 \ge \sin\theta,

then:

|2 - \sin\theta| = 2 - \sin\theta

In order to maximize

2 - \sin\theta, \sin\theta

should be minimum.

The minimum value of

\sin\theta

is -1 .

\therefore

The maximum value of

2 - \sin\theta

is

2 - (-1) = 3

.

CASE 2: If

2 - \sin\theta < 0 \Rightarrow 2 < \sin\theta,

which is not possible.Therefore, the maximum value of

|2 - \sin\theta|

is

|3| = 3.

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