Question

If 1 + `cosx` - 2`sin^2x` = 0 , what is the value of `x`?

Answer 1

`x = { pm pi +2k pi} uu {pm pi/3 + 2k pi}` for `k = 0,pm1,pm2,pm3,...`

Explanation:

Making `sin(x)^2=1-cos(x)^2` and `y = cos(x)` we obtain

`1+y-2(1-y^2)=0`

Solving for `y` we have `{y=-1,y=1/2}` so the solutions for `x` must obey

`cos(x) = -1` or `cos(x) = 1/2`

Solving for `x` we obtain

`x = pm pi +2k pi` for `cos(x) = -1` and
`x = pm pi/3 + 2k pi` for `cos(x) = 1/2`
for `k = 0,pm1,pm2,pm3,...`