Checkout JEE MAINS 2022 Question Paper Analysis : Checkout JEE MAINS 2022 Question Paper Analysis :

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

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