Question

The domain of sec 5x is.​

Answer 1

Given:

F(x) = Sec(5x)

To Find:

Domain of F(x)

Solution:

Domain of a function is defined as the the values which goes into the function. The domain of  function is  defined as the complete set of possible values of the independent variable which gives a possible and defined output.

Sec (x) is equal to  inverse  of cos(x)

$sec (x) = \frac{1}{Cos(x)}$

cos(x) ≠ 0 is the domain for sec(x).

If cos(x) = 0 sec(x) is undefined.

cos(x) = 0 at  x = (n+1)$\frac{\pi }{2}$

That  is the odd multiples of $\frac{\pi }{2}$

Cos(5x) = 0 at x = (n+1)$\frac{\pi }{10}$

Hence  the domain of Sec(5x) is R - (n+1)$\frac{\pi }{10}$