Question #16d46

1 Answer
Apr 17, 2017

Answer:

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

Explanation:

Use trig identities:
#2sin^2x = 1 - cos 2x#
#2cos^2 x = 1 + cos 2x#
In this case:
#tan (x/2) = sin (x/2)/(cos (x/2)#
Find #sin (x/2)# and #cos (x/2)# in terms of cos x.
#sin^2 (x/2) = (1 - cos x)/2# -->
#sin (x/2) = +- sqrt((1 - cos x))/(sqrt2)#.

#cos^2 (x/2) = (1 + cos x)/2#.
#cos (x/2) = +- sqrt((1 + cos x)/(sqrt2)#.
#tan (x/2) = sqrt((1 - cos x)/(1 + cos x))#.