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The minimum value of 2sin2θ + 3cos2θ is ?

A. 0

B. 3

C. 2

D. 1

Answer: Option C

Solution(By Examveda Team)

Let x = 2sin2θ + 3cos2θ
⇒ x = 2sin2θ + 2cos2θ + cos2θ
⇒ x = 2(sin2θ + cos2θ) + cos2θ
⇒ x = 2 + cos2θ     [since sin2θ + cos2θ = 1]
Therefore x will be the minimum when cosθ = 0. i.e. minimum value of x will 2

Alternative Solution:
2sin2θ + 3cos2θ
Minimum value is 2,
[If x sin2θ + y cos2θ, If x > y, then x will be always maximum value and y is minimum if y > x, vice versa will happen]

This Question Belongs to Arithmetic Ability >> Trigonometry

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Comments ( 1 )

  1. KDG FIRE
    KDG FIRE :
    2 years ago

    Cos 0° = 1
    Then 2+ cos2 = 2+(1)2= 2+1=3
    And in alternative solution
    When y>x then y is minimum
    And here x=2 and y=3
    Hence y>x
    Then minimumvalue is y=3

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