Question

How do you solve `cos(x/2) - sin(x) = 0`?

Answer 1

`pi + 2kpi`
`2kpi`
(5pi)/3 + 2kpi

Explanation:

Use trig identity: `sin x = 2sin (x/2).cos (x/2)`. We get:
`cos (x/2)- sin (x/2).cos (x/2) = 0`
`cos (x/2)(1 - 2sin x) = 0`
a. `cos (x/2) = 0` -->arc `x/2 = pi/2` and arc `x = (3pi)/2` -->
`x = pi` and `x = 3pi.`
General answer -->`x = pi + 2kpi`
b.`sin (x/2) = 1/2`.
Trig table and unit circle give:
`x/2 = pi/6` and `x/2 = (5pi)/6` -->
`x = (2pi)/6` and `x = (5pi)/3`
General answers:
`x = pi + 2kpi`
`x = 2kpi`
`x = (5pi)/3 + 2kpi`