Find all solutions of the equation in the interval [0,2pi). 4sinx = -cos²(x)+1. Write your answer in radians in terms of pi

Answer 1

sin^2x + cos^2x = 1

4sinx = -cos^2 + sin^2x + cos^2x = sin^2x

sin^2x -4sinx = 0

sinx(sinx-4) = 0

sinx = 0 (ignore sinx=4 because the sine of any angle is always < 1)

x= 0 or pi