Question

Find the least value of 2 sin^2 A+3 cos^2 A
$please explain in detail$

​

Answer 1

Answer:

Let

y

=

2

sin

2

θ

+

3

cos

2

θ

⇒

y

=

2

sin

2

θ

+

2

cos

2

θ

+

cos

2

θ

⇒

y

=

2

(

sin

2

θ

+

cos

2

θ

)

+

cos

2

θ

⇒

y

=

2

+

cos

2

θ

So y will be minimum when

cos

2

θ

=

0

Hence

y

min

=

2

Step-by-step explanation:

Answer 2

Step-by-step explanation:

given, 2sin

2

θ+3cos

2

θ

=2−2cos

2

θ+3cos

2

θ

=2+cos

2

θ

Since we know that −1≤cosθ≤1 then 0≤cos

2

θ≤1,

So minimum value of cos

2

θ=0

Hence,minimum value of 2sin

2

θ+3cos

2

θ=2

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