Question

What is the least value of 9 sin² θ + 16 cos² θ ?

Answer 1

Correct Answer - Option 2 : 9

Concept used :

sin2 θ = 1 - cos2 θ

Calculations :

9 sin2 θ + 16 cos2 θ = 9 sin2 θ + 16 ( 1 - sin2 θ) 

⇒ 9 sin2 θ + 16 - 16 sin2 θ

⇒ -7 sin² θ + 16 

⇒ -7 + 16         (for least value of the equation value of sin² θ must be equal to 1)

⇒ 9 

∴ Option 2 will be the correct choice.