Answer

Verified

455.4k+ views

**Hint:**

Arc functions are also termed as arcus functions, anti-trigonometric functions, inverse trigonometric functions or cyclometric functions. The inverse trigonometry functions have major applications in the field of engineering, physics, geometry and navigation.

There are particularly six inverse trig functions for each trigonometric ratio. The inverse of six important trigonometric functions are:

Arcsine

Arccosine

Arctangent

Arc cotangent

Arc secant

Arc cosecant

Arc of some trigonometric function is the same as the inverse of the function. Arc prefix is commonly used to name the trigonometric functions. For example, \[\arcsin x\] = \[\dfrac{1}{2}\]means the angle whose sine is making \[\dfrac{1}{2}\]. Thus, we can say that \[{{\sin }^{-1}}(x)\]= \[\dfrac{1}{2}\] or x = \[{{30}^{\circ }}\].

To solve this question, find the range of all three trigonometric functions and add them to find the right answer.

**Complete step by step solution:**

Step 1: Let us first find the range of those three trigonometric functions separately.

Since, we know \[\arcsin x+\arccos x\] = \[\dfrac{\pi }{2}\]

Therefore, range of \[\arctan x\] is (\[-\dfrac{\pi }{2}\], \[\dfrac{\pi }{2}\])

Step 2: Minimum value of \[\arcsin x+\arccos x+\arctan x\] = \[\dfrac{\pi }{2}\] + (\[-\dfrac{\pi }{2}\]) = 0

Maximum value of \[\arcsin x+\arccos x+\arctan x\] = \[\dfrac{\pi }{2}\]+\[\dfrac{\pi }{2}\] = \[\pi \]

Hence, the range of \[\arcsin x+\arccos x+\arctan x\] = (0, \[\pi \])

**Note:**

To solve this question, the students should be familiar with trigonometric functions. The basics of trigonometry values are a must. Try to visualise such questions through graphs that can perform such trigonometric functionalities. Once you get familiar with trigonometric graphs and functions you can easily find the values of inverse trigonometric functions. Also, for range, observe the round brackets () are used to write the range as the values 0 and \[\pi \]are not included since the range of \[\arctan x\] is (\[-\dfrac{\pi }{2}\], \[\dfrac{\pi }{2}\])

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?

What percentage of the solar systems mass is found class 8 physics CBSE

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

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

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

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

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

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE