Question

The general solution of the equation tan θ tan 2θ = 1 is given by ______ 

Options

• `(2n + 1)pi/6,` n ∈ I

• `npi + pi/6`, n ∈ I

• `npi - pi/6`, n ∈ I

• `npi ± pi/6`, n ∈ I

Answer 1

The general solution of the equation tan θ tan 2θ = 1 is given by `underline(npi ± pi/6, n ∈ I`.

Explanation:

tan θ tan 2θ = 1

∴ `tantheta (2tantheta)/(1 - tan^2theta) = 1`

∴ `2tan^2theta = 1 - tan^2theta`

∴ `3tan^2theta = 1`

∴ `tan^2theta = 1/3 = tan^2(pi/6)`

∴ `theta = npi ± pi/6` ..........[∵ tan²θ - tan²α ⇒ θ = nπ ± α]