Question

If 2 cos^2 x +sinx =2 , find the value of x​

Answer 1

2cos²x + sin x = 2

2(1 - sin²x) + sin x - 2 = 0

2 - 2 sin²x + sin x - 2 = 0

2 sin²x - sin x = 0

sin x (2 sin x - 1) = 0

=> sin x = 0 or sin x = 1 / 2

I.e., sin x = sin 0 or sin x = sin (π / 6)

=> x = nπ or x = nπ + (-1)ⁿ · π / 6,

where n is an integer.