यदि `alpha = tan^(-1)(1/2)+tan^(-1)(1/3)`,
` beta = cos^(-1)(2/3)+cos^(-1)(sqrt5/3)`
तथा `gamma = sin^(-1)[sin.((2pi)/3)]+1/2 cos^(-1)[cos((2pi)/3)]`
`cos ( alpha+beta + gamma)`का मान होगा

Options

A. `cos((5 pi)/12)`
B. `cos((17 pi)/12)`
C. `cos(pi/12)`
D. `cos ((11 pi)/12)`

Answer

B

Explanation

`cos(alpha+ beta+gamma) = cos(pi/4 + pi/2 + (2pi)/3)`
` = cos((7pi)/6 + pi/4) = cos((17 pi)/12)`