If `sin^2theta_1+sin^2theta_2+sin^2theta_3=0,` then which of the following is not the possible value of `costheta_1+costheta_2+costheta_3?` 3 (b) `-3` (c) `-1` (d) `-2`

Options

A. 3
B. -3
C. -1
D. -2

Explanation

To solve the problem, we start with the given equation:

\[ \sin^2 \theta_1 + \sin^2 \theta_2 + \sin^2 \theta_3 = 0 \]

### Step 1: Analyze the equation
Since the sine squared function is always non-negative (i.e., \(\sin^2 \theta \geq 0\) for any angle \(\theta\)), the only way for the sum of three non-negative numbers to equal zero is if each individual term is zero. Therefore, we conclude:
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