Find the general solution of the equation

[Hint: Put which gives ]

Given equation is:

We need to solve the above equation.

If we can convert this to a single trigonometric ratio, we can easily give its solution by using the formula.

For this,

Let, r sinα = √3 – 1 and r cosα = √3 + 1

∴

And,

Hence, equation can be rewritten as-

∴ r(sinα cos θ + r cosα sin θ) = 2

⇒ 2√2 sin (θ + α) = 2

⇒ sin(θ + α) = 1/√2 = sin π/4

We know that: General solution of trigonometric equation

sin x = sin α is given as –

x = nπ + (-1)ⁿα , n ∈ Z

∴ θ + α = nπ + (-1)ⁿ(π/4)

⇒ θ = {nπ + (-1)ⁿ(π/4) – α} ,where tan α = and n ∈ Z