sin x + 1 = 2 × (cos x)²

sin x + 1 = 2 × (1 - (sin x)²)

sin x + 1 = 2 – 2(sin x)²

2(sin x)² + sin x - 1 = 0

Consider a=sin x

So, the equation will be

2a²+a-1=0

From the equation a=0.5 or -1

Which implies

Sin x=0.5 or sin x=(-1)

Therefore x=30° or 270°

But for x=270° our equation will not be defined as cos (270° )=0

So, the solution for x=30°

According to trigonometric equations

If sin x=sin a

Then x=nπ – na

Here sin x=sin30

So, x=nπ + (-1)ⁿ × 30

For n=0, x=30 and n=1,x=150° and for n=2,x=390

Hence between 0 to 2π there are only 2 possible solutions.