Answer

Verified

380.7k+ views

**Hint:**For solving this question you should know about finding the values of inverse trigonometric values of the given functions. But if it is given to find the value of a trigonometric function, then we find the trigonometric value of that function and then we add them according to the given sequence.

**Complete step by step answer:**

According to our question t is asked of us to find the correct option for the value of $f\left( x \right)={{\sec }^{-1}}x+{{\tan }^{-1}}x$. As we know that if any question is asking for the values of trigonometric functions, then we directly put the value of that function there and get our required answer for that. But if it is given to find the angles of them, then we find the original function (trigonometric function) for that value and then we get the angle of that by comparing it with each other. And if it is asked directly without any angle, then we always use the general formulas of trigonometry for solving this. And we will solve that according to the given sequence of calculations.

So, if we look at our question, then,

$f\left( x \right)={{\sec }^{-1}}x+{{\tan }^{-1}}x$

And the value of $\sec x$ and $\operatorname{cosec}x$ does not lie between +1 and -1.

If $\phi \left( x \right)={{\sec }^{-1}}x$, then we know that, $x\in \left( -\infty ,-1 \right]\cup \left[ 1,\infty \right)$.

Also $g\left( x \right)={{\tan }^{-1}}x$, then $x\in R$.

Hence for holding $f\left( x \right)={{\sec }^{-1}}x+{{\tan }^{-1}}x$, we have $x\in \left( -\infty ,-1 \right]\cup \left[ 1,\infty \right)$.

**So, the correct answer is “Option C”.**

**Note:**While solving these type problems you have to always mind that if the value of inverse trigonometric function is asked, then find that and if it is asked for the angle, then find it by comparing, if that is asking for the trigonometric function value to solve any problem, then give that, but if no angles are given, then always use the general trigonometric formulas.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell