Find sinx2 cosx2 and tanx2 from the given information secx

Find sin(x/2), cos(x/2), and tan(x/2) from the given information. sec(x) = 4/, 270 degree

Solution

sec x=4/3

cos x=1/sec x= 3/4

sin(x/2)= sqrt((1-cosx)/2) = sqrt(1/4/2)= 1/(2sqrt2)

cos(x/2)=-sqrt((1+cosx)/2)= - sqrt(7/8)= (- 1/2)(sqrt7/2)

tan(x/2)= sin(x/2)/cos(x/2)= - sqrt7