What is $(p + q + r)$ equal to?

Question

Question

Consider the following for the three (03) items that follow: Let $p = sin 3 5^{\circ}$ , $q = sin 2 5^{\circ}$ and $r = sin (- 9 5^{\circ})$ .

This question was previously asked in

NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)

Answer 1

Calculation:

Given,

Let, and

We need to find the value of p + q + r .

First, we know that:

.

Thus, the expression p + q + r becomes:

.

Using the identity for the sum of two sine functions:

.

Substitute and

.

Since , we get:

.

Now, we know that:

.

Therefore:

.

∴ The value of p + q + r is 0.

Hence, the correct answer is Option 0.

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