Question

How do you find cos x/2 if cos x= -31/49 using the half-angle identity?

Answer 1

`+- 3/7`

Explanation:

Use trig identity: `cos x = 2cos^ (x/2) - 1`
`cos x = - 31/49 = 2cos^2 x - 1`
`2cos^2 x = 1 - 31/49 = 18/49`
`cos^2 (x/2) = 9/49` --> `cos (x/2) = +- 3/7`
Both answers are correct.
Check.
`x/2 = 3/7` --> `x/2 = 64^@62` --> `x = 129^@25` --> `cos x = -31/49`
`x/2 = -3/7` --> `x/2 = 115^@37` --> `x = 230.75`--> `cos x = - 31/49`. OK