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]
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Comments ( 1 )
Related Questions on Trigonometry
A. x = -y
B. x > y
C. x = y
D. x < y
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