Question

If n is any integer, then the general solution of the equation `cos x - sin x = 1/sqrt(2)` is

Options

• `x = 2npi - pi/12` or `x = 2npi + (7pi)/12`

• `x = npi - pi/12`

• `x = 2npi + pi/12` or `x = 2npi - (7pi)/12`

• `x = npi + pi/12` or `x = npi - (7pi)/12`

Answer 1

`x = 2npi + pi/12` or `x = 2npi - (7pi)/12`

Explanation:

Given equation is `cos x - sin x = 1/sqrt(2)`

Dividing equation by `sqrt(2), 1/sqrt(2) cos x - 1/sqrt(2) sin x = 1/2`

⇒ `cos (pi/4 + x) = cos  pi/3`

⇒ `pi/4 + x = 2npi +- pi/3; x = 2n pi + pi/3 - pi/4 = 2n pi + pi/12`

or `x = 2n pi - pi/3 - pi/4 = 2n pi - (7pi)/12`.