sin2 theta cos2 theta 1 cos theta REQUIRED Algebraically

sin^2 theta - cos^2 theta = 1 + cos theta REQUIRED Algebraically solve the given equation on the interval 0 lessthanorequalto theta lessthanorequalto 2pi.

Solution

let us assume theta= \'x\'

so the given equation becomes sin^2x -cos^2x = 1+cosx ----->1

from identity sin^2x +cos^2x =1

so sin^2x = 1-cos^2x

plug it in equation1

1-cos^2x-cos^2x = 1+cosx

1-2cos^2x =1+cosx

2cos^2x+cosx=0

cosx(2cosx+1)=0

cosx=0 or (2cosx +1)=0

x= pi/2,3pi/2 or 2cosx =-1

x =pi/2,3pi/2 or cosx =-1/2

x=pi/2,3pi/2 or x= 2pi/3, 4pi/3

the value of theta are pi/2,2pi/3,4pi/3,3pi/2