What is $(p+q+r)$ equal to?

Calculation:

Given,

Let\(p = \sin 35^\circ \),\(q = \sin 25^\circ \) and \(r = \sin(-95^\circ) \)

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

First, we know that:

\( \sin(-95^\circ) = -\sin(95^\circ) \).

Thus, the expression p + q + r becomes:

\( p + q + r = \sin 35^\circ + \sin 25^\circ - \sin 95^\circ \).

Using the identity for the sum of two sine functions:

\( \sin A + \sin B = 2 \sin \left( \frac{A + B}{2} \right) \cos \left( \frac{A - B}{2} \right) \).

Substitute \(A = 35^\circ \) and \(B = 25^\circ \)

\( \sin 35^\circ + \sin 25^\circ = 2 \sin 30^\circ \cos 5^\circ \).

Since \(\sin 30^\circ = \frac{1}{2} \), we get:

\( \sin 35^\circ + \sin 25^\circ = \cos 5^\circ \).

Now, we know that:

\( \sin 95^\circ = \cos 5^\circ \).

Therefore:

\( p + q + r = \cos 5^\circ - \cos 5^\circ = 0 \).

∴ The value of p + q + r  is 0.

Hence, the correct answer is Option 0.