Question

Solution of the equation 3 tan(θ – 15) = tan(θ + 15) is

Options

• θ = `(npi)/2 + (-1)^n  pi/4`

• θ = `npi + (-1)^n  pi/3`

• θ = `npi - pi/3`

• θ = `npi - pi/4`

Answer 1

θ = `(npi)/2 + (-1)^n  pi/4`

Explanation:

Given, 3 tan(θ – 15) = tan(θ + 15). `tan A/tan B = 3/1`,

Where A = θ + 15°, B = θ – 15°

On applying componendo and dividendo, we get

⇒ `(tan A + tan B)/(tan A - tan B) = (3 + 1)/(3 - 1)`

⇒ `(sin A/cos A + sin B/cos B)/(sin A/cos A - sin B/sin B)` = 2

⇒ `(sin (A + B))/(sin (A - B))` = 2

⇒ sin 2θ = 2 sin 30°

⇒ sin 2θ = `2 * 1/2 = 1 = sin  pi/2`

⇒ 2θ = `npi + (-1)^n  pi/2`

⇒ θ = `(npi)/2 + (-1)^n  pi/4`.