Topic : Solve the Expression
Question : 4(1+Sin x) = Cos² x
Solution :
4(1+Sin x) = Cos² x , We Know that Cos² x = 1-Sin² x => (1-Sin x)(1+Sin x)
4(1+Sin x)- Cos² x = 0
4(1+Sin x)- (1-Sin² x) = 0
4(1+Sin x)- (1-Sin x)(1+Sin x) = 0
(1+Sin x)[4-(1-Sin x)]=0
(1+Sin x)(3+Sin x)=0
Either 1+Sin x = 0 or 3+Sin x=0
either Sin x = -1 or Sin x = - 3
either x = - π/2 , 3π/2
As Sine varies from -1 to 1. Minimum value of Sine θ can never become -3
So we have Sine θ = -1
hence θ = - π/2 or 3π/2
in the interval [0,2π].
