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Verify the trigonometric identity: cos(alpha + beta)*cos(gamma) - cos(beta + gamma)*cos(alpha) = sin(beta)*sin(gamma - alpha). Which statement is correct?

1. The identity is true for all alpha, beta, gamma.
2. The identity holds only when alpha = gamma.
3. The identity holds only when beta = 0.
4. The identity is never true.

Correct answer: The identity is true for all alpha, beta, gamma.

Solution

Expanding the left side and simplifying reproduces sin(beta)*sin(gamma-alpha), so the identity holds universally.

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