Find cosx2 given cotx 3 pi2 x piSolution given cotx 3 pi

Find cos(x/2), given cot(x) = -3

pi/2 < x < pi

, given cot(x) = -3

pi/2 < x < pi

x is in IInd quadrant

tanx = -1/3

hypotenuse = sqrt(1 +3^2) = sqrt(10)

cosx = - 3/sqrt(10)

cos(x/2) = sqrt{ (1 +cosx)/2 }

= sqrt{( 1 -3/sqrt(10))/2 }

= sqrt(sqrt(10) -3)/2sqrt(10) )