1.

The expression `cos^(2)(alpha + beta + gamma) + cos^(2)(beta + gamma) + cos^(2)alpha - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma)` isA. independent of `alpha`B. independent of `beta`C. dependent on `gamma` onlyD. dependent on `alpha, beta, gamma`

Answer» Correct Answer - A::B
`E = cos^(2)alpha + cos^(2)(beta + gamma) + cos^(2)(alpha + beta + gamma) - 2cos alpha cos(beta + gamma)cos(alpha + beta + gamma)`
`= cos^(2)alpha + cos^(2)(beta + gamma) + cos^(2)(alpha + beta + gamma) - [(cos(alpha + beta + gamma) + cos(alpha - beta - gamma)).cos(alpha + beta + gamma)]`
`= cos^(2)alpha + cos^(2)(beta + gamma) - [cos(beta + gamma - alpha) cos (beta + gamma + alpha))`
`= cos^(2)alpha + cos^(2)(beta + gamma) - (cos^(2)(beta + gamma) - [cos^(2)(beta + gamma) - sin^(2)alpha ] = 1`


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