Question

If the value of (1 - cos 2A)/(1 + cos 2A) = 9/16, then find the value of sin A + sec A?
1. 37/20
2. 12/17
3. 37/25
4. 13/12

Answer 1

Correct Answer - Option 1 : 37/20

Given:

(1 - cos 2A)/(1 + cos 2A) = 9/16

Identity used:

(1 - cos 2A)/(1 + cos 2A) = tan² A

In a right angled triangle;

Tan θ = Perpendicular/Base

Sec θ = Hypotenuse/Base

Calculation:

(1 - cos 2A)/(1 + cos 2A) = tan2 A

Tan2 A = 9/16

⇒ Tan A = 3/4

⇒ Sin A = 3/5

⇒ Sec A = 5/4

Sin A + Sec A = 3/5 + 5/4

⇒ (12 + 25)/20 = 37/20

∴ The value of sin A + sec A is 37/20.