Question

Which of the following describes the domain of y = tan x, where n is any integer? A.x≠2nπ B. x≠π/2+nπ C. x≠nπ D.x≠nπ/2

Answer 1

Y=tanx=sinx/cosx we cant divide by 0 so

cosx=0 would be a problm
cosx=0 when x=pi/2,3pi/2,...(2n+1)pi/2
(2n+1)pi/2=(2npi+pi)/2=2npi/2+pi/2=npi+pi/2
so its B

Answer 2

The correct answer is: Option (B)  $\frac{\pi}{2} + n\pi$

Explanation:

Given function:

$y = tan(x)$

We know that,

$tan(x) = \frac{sin(x)}{cos(x)}$

To find the domain, put the "denominator" equal to zero, as follows:

$cos(x) = 0$

Now ask yourself the following question to find domain: For what values of x, will $cos(x)$ be equal to 0? Well, for $x = \frac{\pi }{2}, \frac{3\pi}{2},\frac{5\pi}{2},..., \frac{\pi}{2}(1+2n)$ where n = any integer.

Therefore, the domain of y = tan(x) is:

$\frac{\pi}{2}(1+2n)\\\frac{\pi}{2} + \frac{2n\pi}{2}$

$\frac{\pi}{2} + n\pi$ (Option B)