Find all solutions of the equation in the interval 0 2 pi 2s

Find all solutions of the equation in the interval [0, 2 pi). -2sinx + cos 2x = 1 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

Solution

Given equation is

-2*sinx + cos^2x = 1

-2*sinx + cos^2x - 1 = 0

-2*sinx + (1 - sin^2x) - 1 = 0

-sin^2x - 2*sinx = 0

sinx(sinx + 2) = 0

sinx = 0=======> x = 0, pi

sinx = -2 =======> Not possible