What is the minimum value of 4sin2θ + 5cos2θ is

Question: What is the minimum value of 4sin2θ + 5cos2θ is-Solution:Let,⇒ x = 4sin2θ + 5cos2θ⇒ x = 4sin2θ + 4cos2θ + cos2θ⇒ x = 4(sin2θ + cos2θ) + cos2θ⇒ x = 4 + cos2θ [sin2θ + cos2θ = 1]⇒ x = 4 + 0∴ x = 4The minimum value of x depends on the minimum value of cos2θSince the minimum value of cos2θ is 0, So the minimum value of x is 4.