Question

Find the maximum and minimum value of 7 Sin²θ + 17 Cos²θ 
1. 1, 0
2. 12, 7
3. 7, 17
4. 17, 7

Answer 1

Correct Answer - Option 4 : 17, 7

Given:

7 Sin2θ + 17 Cos2θ 

Concept used:

Sin2θ + Cos2θ = 1

Maximum value of Cos2θ = 1

Minimum value of Cos2θ = 0

Calculation:

7 Sin2θ + 17 Cos2θ 

⇒ 7 Sin2θ + 7 Cos2θ + 10 Cos2θ 

⇒ 7 (Sin2θ + Cos2θ) + 10 Cos2θ 

⇒ 7 + 10 Cos2θ 

Maximum value of Cos2θ = 1

⇒ Maximum value of 7 + 10 Cos2θ

⇒ 7 + 10

⇒ 17

Minimum value of Cos2θ = 0

⇒ Minimum value of  7 + 10 Cos2θ

⇒ 7 + 0

⇒ 7

∴ Option D is correct option.