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

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

Solution

cos^2x = 1-sinx

we can use trig identity : cos^2x = 1-sin^2x

So, 1 -sin^2x = 1-sinx

(1-sinx)(1+sinx) = (1-sinx)

(1-sinx)( 1+sinx -1 ) =0

sinx(1- sinx)=0

sinx =0

x =0 , pi

1-sinx =0

sinx =1 -----> x= pi/2

Solution : x=0, pi/2 , pi