Find the exact value of cos cot1squareroot 3 sin1 12 Show a

Find the exact value of cos [cot^-1(-squareroot 3) + sin-1 (-1/2)]. Show any necessary work.

Solution

cos[ cot^-1(-sqrt3) +sin^-1(-1/2)]

cot^-1(-sqrt3) = pi -pi/6 = 5pi/6

sin^-1( -1/2) = 2pi - pi/6 = 11pi/6

cos[ cot^-1(-sqrt3) +sin^-1(-1/2)] = cos( 5pi/6 +11pi/6)

= cos( 16pi/6)

= cos( 8pi/3) = cos( 2pi +2pi/3)

=cos2pi/3 = - 1/2