Find sinx2 cosx2 and tanx2 from the given information cosx

Find sin(x/2), cos(x/2), and tan(x/2) from the given information. cos(x) = - 24/25, 180 degree

Solution

tanx = sqrt 2 ; 0<x < pi/2

cos(x) = 1/sqrt3

a) sin(x/2) = sqrt[ (1-cosx)/2]

= sqrt[( 1- 1/sqrt3)/2]

= sqrt[(sqrt3-1)/2sqrt3]

cos(x/2) = sqrt[ (1+ cosx)/2]

= sqrt[(1 + 1/sqrt3)/2]

= sqrt[(sqrt3 +1)/2sqrt3]

c) tan(x/2) = sin(x/2) /cos(x/2)

= sqrt[(sqrt3-1)/2sqrt3] /sqrt[(sqrt3 +1)/2sqrt3]

= sqrt[( sqrt3 -1)/(sqrt3 +1)]