If secθ + tanθ = 2, then what is the value of 3secθ + 4?

Correct option is A

Given:

secθ + tanθ = 2

Concept Used:

Identity: sec²θ - tan²θ = 1 

Solution: 

secθ + tanθ = 2 ............ equation(1)

(secθ + tanθ)(secθ - tanθ) = 1 

2(secθ - tanθ) = 1 

(secθ - tanθ)  = 1/2 .......equation (2)

Add equation (2) and (2) 

2secθ  =  2 + 1/2 

​secθ  = $$\frac{5}{4}$$​

Then the value of 3secθ + 4  = $$3 \times \frac{5}{4} + 4 = \frac{15}{4} + 4 = \frac{31}{4}$$​​