Question

Find the domain of \[\sec 2x\] ?

Answer 1

Hint: Domain of any function is the values possible for that function which means, after entering the values you will get a result and when talking with the trigonometric identities, here also the domain plays the same role means either you put an angle or any integer value or real value, the value should provide a result with that function.

Complete step-by-step answer:
The given question is \[\sec 2x\]
For the given trigonometric identity we know that this function is not defined for any multiple of ninety degree because at ninety degree the value comes as infinity.
Now we know that this trigonometric identity repeats its behavior at \[n\pi \] here “n” denotes any integer value.
Now concluding the equation in mathematical form we get:
 \[ \Rightarrow 2x \ne \dfrac{\pi }{2} + n\pi \]
Here we can transfer “2” from left hand side to right hand side, we get:
 \[ \Rightarrow x \ne \dfrac{\pi }{4} + \dfrac{{n\pi }}{2}\]
So the final accepted domain for identity is every possible values of “x” except \[x \ne \dfrac{\pi }{4} + \dfrac{{n\pi }}{2}\]
So, the correct answer is “ \[x \ne \dfrac{\pi }{4} + \dfrac{{n\pi }}{2}\] ”.

Note: Here after getting the domain you can randomly check for any value which comes under your mind except the given condition values, and then you can cross check your answer and be satisfied with what you have done.
The given question needs the domain for which you can also draw the graph for the given trigonometric identity and then can get the domain for the function, but as any conditions were not given in the question then the above process is more suitable to solve and get the domain.