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If f(x) =|{:(cos (x+alpha),cos(x+beta),c...

If f(x) =`|{:(cos (x+alpha),cos(x+beta),cos(x+gamma)),(sin (x+alpha),sin(x+beta),sin(x+gamma)),(sin(beta+gamma),sin(gamma+alpha),sin(alpha+beta)):}|` then `f(theta)-2f(phi)+f(psi)` is equal to

A

(A)0

B

(B)`alpha-beta`

C

(C)`alpha+beta+gamma`

D

(D)`alpha+beta+-gamma`

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The correct Answer is:
A
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