If (sec θ + tan θ) = 4, then find the value of sin θ.1. 17/82. 8

1.	If (sec θ + tan θ) = 4, then find the value of sin θ.1. 17/82. 8/173. 17/154. 15/17
Answer» Correct Answer - Option 4 : 15/17 Given: sec θ + tan θ = 4 ----(i) Formula used: sec²θ – tan² θ = 1 (a² – b²) = (a + b)(a – b) sec θ = Hypotenuse/Base sin θ = Perpendicular/Hypotenuse Calculations: Using the given identities, ⇒ (sec θ + tan θ)(sec θ – tan θ) = 1 ⇒ 4 × (sec θ – tan θ) = 1 ⇒ (sec θ – tan θ) = 1/4 (ii) Adding (i) and (ii), ⇒ 2sec θ = 17/4 ⇒ sec θ = 17/8 sin θ = √(17² – 8²)/17 ⇒ sin θ = 15/17 ∴ The value of sin θ is 15/17

If (sec θ + tan θ) = 4, then find the value of sin θ.1. 17/82. 8/173. 17/154. 15/17

Answer» Correct Answer - Option 4 : 15/17

Given:

sec θ + tan θ = 4 ----(i)

Formula used:

sec²θ – tan² θ = 1

(a² – b²) = (a + b)(a – b)

sec θ = Hypotenuse/Base

sin θ = Perpendicular/Hypotenuse

Calculations:

Using the given identities,

⇒ (sec θ + tan θ)(sec θ – tan θ) = 1

⇒ 4 × (sec θ – tan θ) = 1

⇒ (sec θ – tan θ) = 1/4 (ii)

Adding (i) and (ii),

⇒ 2sec θ = 17/4

⇒ sec θ = 17/8

sin θ = √(17² – 8²)/17

⇒ sin θ = 15/17

∴ The value of sin θ is 15/17