The minimum and maximum value of 12 sin2θ +13 cos2θ is1. 10 and 12

1.	The minimum and maximum value of 12 sin2θ +13 cos2θ is1. 10 and 122. 13 and 153. 12 and 134. 9 and 11
Answer» Correct Answer - Option 3 : 12 and 13 Trigonometry identity used: Sin²θ + cos²θ = 1 Calculation: 12 sin²θ + 13 cos²θ = 12 sin²θ + 12 cos²θ + cos²θ = 12 (sin²θ + cos²θ) + cos²θ = 12 + cos²θ For minimum value, Minimum value of cosθ = –1 But cos²θ ≥ 0, when θ = 90° So, cos0° = 1, Then, required minimum value = 12 + 0 = 12. For the maximum value, Maximum value of cosθ = 1 And cos²θ =1 Then, required maximum value, = 12 + 1 = 13 ∴The minimum and maximum values of 12 sin²θ +13 cos²θ are 12 and 13.

The minimum and maximum value of 12 sin2θ +13 cos2θ is1. 10 and 122. 13 and 153. 12 and 134. 9 and 11

Answer» Correct Answer - Option 3 : 12 and 13

Trigonometry identity used:

Sin²θ + cos²θ = 1

Calculation:

12 sin²θ + 13 cos²θ

= 12 sin²θ + 12 cos²θ + cos²θ

= 12 (sin²θ + cos²θ) + cos²θ

= 12 + cos²θ

For minimum value,

Minimum value of cosθ = –1

But cos²θ ≥ 0, when θ = 90°

So, cos0° = 1,

Then, required minimum value

= 12 + 0

= 12.

For the maximum value,

Maximum value of cosθ = 1

And cos²θ =1

Then, required maximum value,

= 12 + 1 = 13

∴The minimum and maximum values of 12 sin²θ +13 cos²θ are 12 and 13.