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

Find all solutions of the equation in the interval [0, 2 pi). 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. x =

Solution

We have given equation is cos²x =1+sinx

cos²x =1+sinx

1-sin²x=1+sinx since substituting cos²x=1-sin²x

sin²x+sinx =0 since taking right side value of the equaton into left side value

sinx(sinx+1)= 0

sinx=0 and sinx=-1

x=0 degrees and x=270 degrees

Converting into radians x=[0 ,3pi/2]

Therefore

The solutions of the given equation is x=[0 ,3pi/2] in radians