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

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) The value of cos(alpha+beta+gamma) is equal to (A) cos((5pi)/12) (B) cos ((7pi)/12) (C) -cos(pi/12) (D) -cos ((7pi)/12)

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) The value of cos(alpha+beta+gamma) is equal to (A) cos((5pi)/12) (B) cos ((7pi)/12) (C) -cos(pi/12) (D) -cos ((7pi)/12)

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) then sincot^-1 tancos^-1 (sin gamma) is equal to (A) 2singamma (B) sin(gamma/2) (C) 1/2 sin gamma (D) cosgamma

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) sincot^-1 tancos^-1 (sin gamma) is equal to (A) 2singamma (B) sin(gamma/2) (C) 1/2 sin gamma (D) cosgamma

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) then cosalpha+cosbeta+cosgamma is equal to (A) (sqrt(2)-1)/2 (B) (sqrt(2)+1)/2 (C) (sqrt(2)+sqrt(3))/2 (D) ((sqrt(3)-sqrt(2))/2)

Let alpha = tan^-1 (1/2)+tan^-1(1/3) , beta=cos^-1(2/3)+cos^-1(sqrt5/3) , gamma=sin^-1(sin((2pi)/3))+1/2cos^-1(cos((2pi)/3)) cosalpha+cosbeta+cosgamma is equal to (A) (sqrt(2)-1)/2 (B) (sqrt(2)+1)/2 (C) (sqrt(2)+sqrt(3))/2 (D) ((sqrt(3)-sqrt(2))/2

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then

If alpha = sin^(-1)(sqrt(3)/2)+sin^(-1)(1/3) , beta =cos ^(-1)(sqrt(3)/2)+cos^(-1)(1/3) then