Question

Question #16d46

Answer 1

`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))`.