Question
If 'θ' is an angle less than 120°, what is the value of 'θ' if it satisfies the equation 3cos2θ = 2 + sin2θ.
Solution
Given, 3cos2θ = 2 + sin2θ
Or, 3cos2θ - sin2 θ = 2
Or, 3cos2θ - (1 - cos2 θ) = 2
Or, 4cos2θ = 3
Or, cos2θ = (3/4)
Or, cosθ = √3/2 (Since, in options maximum value of 'θ' is 90o therefore, we will take the positive root only)
Or, cosθ = cos30o
So, θ = 30o
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