Use factoring, the quadratic formula, or identities to solve cos(x)+1=sin^(2)x. Find all solutions on the interval [0, 2pi)

Answer 1

recall that
sin^2 x + cos^2 x = 1
therefore, we use this substitute the sin^2 x at the right side of equation:
cos(x) + 1 = 1 - cos^2 x
cos(x) = -cos^2 x
cos(x) + cos^2 (x) = 0
factoring,
cos(x) [1 + cos(x)] = 0
*for cos(x) = 0, the x values allowed are π/2 and 3π/2.
*for (1 + cos(x)) = 0 or cos(x) = -1, the x value allowed is π.

therefore,
x = π/2, π, 3π/2

hope this helps~ :)