If (1 - tan²θ)/sec²θ = 1/2, then the general value of θ is

1) nπ ± π/6

2) nπ + π/6

3) 2nπ ± π/6

4) None of these

Answer: (1) nπ ± π/6

Solution:

Given,

(1 – tan²θ)/sec²θ = 1/2

Using the identity sec²A – tan²A = 1,

(1 – tan²θ)/(1 + tan²θ) = 1/2

2 – 2 tan²θ = 1 + tan²θ

tan²θ + 2 tan²θ = 2 – 1

3 tan²θ = 1

tan²θ = 1/3

tan²θ = ±1/√3 = tan²(π/6)

As we know if tan²θ = tan²α, then θ = nπ ± α.

Therefore, θ = nπ ± π/6