Question

Find the value of sec 3θ + tan 6θ, if sec (2θ + 40°) = cosec (3θ)
1. 5
2. √3/2
3. 5/√3
4. √3 + 1

Answer 1

Correct Answer - Option 3 : 5/√3

Given :

sec(2θ + 40°) = cosec(3θ)

Formula used :

sec(90° - θ) = cosecθ 

Calculations :

sec(2θ + 40°) = cosec(3θ)

sec(2θ + 40°) = sec(90° - 3θ)

Now 

2θ + 40° = 90° - 3θ 

5θ = 50° 

θ = 10° 

So, 

sec3θ + tan6θ = sec30° + tan60° 

⇒ (2/√3) + √3 

⇒ 5/√3 

∴ Option 3 is the right choice.