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

cos x = - 24 / 25

x lies in 3rd quadrant

applying half angle formula

sin ( x/2 ) = + - sqrt ( 1 - cos x ) / 2

sin ( x/2 ) = + - sqrt ( 1 - ( -24/25 )) / 2 = + - sqrt ( 49/50 ) = +- 7 / sqrt 50

cos ( x/2 ) = + - sqrt ( 1 + cos x ) / 2

cos ( x/2 ) = + - sqrt ( 1 + ( -24/25 )) / 2 = + - 1 / sqrt 50

tan (x/2 ) = + - sqrt ( 1- cos x / 1+cos x )

tan (x/2 ) = + - sqrt ( 49/1 ) = + - 7