Question

The general solution of x satisfying `cot(π/4 - x/3) = sqrt(3)/3` is ______.

Options

• `π/2(12n - 1); n∈I`

• `π/2(12n + 1); n∈I`

• `(-π)/2(12n + 1); n∈I`

• `π/12(12n + 1); n∈I`

Answer 1

The general solution of x satisfying `cot(π/4 - x/3) = sqrt(3)/3` is `underlinebb((-π)/2(12n + 1); n∈I)`.

Explanation:

`cot(π/4 - x/3) = cot  π/3`

⇒ `π/4 - x/3 = nπ + π/3`

⇒ `x/3 = π/4 - nπ - π/3`

= `-π/12 - nπ`

⇒ x = `-π/12(12n + 1), n∈I`