Question

The general solution of cot 4x = –1 is ______.

Options

• x = `nπ + (3π)/4, n ∈ Z`

• x = `(nπ)/4 + (3π)/16, n ∈ Z`

• x = `(nπ)/4 + π/16, n ∈ Z`

• x = `(nπ)/8 + (3π)/16, n ∈ Z`

Answer 1

The general solution of cot 4x = –1 is `underlinebb(x = (nπ)/4 + (3π)/16, n ∈ Z)`.

Explanation:

cot 4x = –1,

∴ tan 4x = –1

= `-tan  π/4` 

= `tan(π - π/4)`

= `tan  (3π)/4`

∴ The general solution is given by:

4x = `nπ + (3π)/4, n ∈ Z`

∴ x = `(nπ)/4 + (3π)/16, n ∈ Z`