Question

If \( \cos \alpha + i \sin \alpha = b \), \( c = \cos \gamma + i \sin \gamma \) and \( b + c + a = 1 \), then \( \cos (\beta - \gamma) + \cos (\alpha - \beta) \) is equal to?

• A. \( \frac{3}{2} \)
• B. \( \frac{3}{5} \)
• C. \( 1 \)
• D. None of these

Hint:

Trigonometric identities can simplify expressions involving sums and differences of angles.

Answer 1

The Correct Option is C

By applying trigonometric identities and simplifying, we find that \( \cos (\beta - \gamma) + \cos (\alpha - \beta) = 1 \).