Question

Find x for which tan inverse 1/x=cot inverse x,holds

Answer 1

Answer:

X=1

Step-by-step explanation:

We can write cot inverse(x) as pi/2- tan inverse (x)

Then by solving we get the value of x i e

X=1

Answer 2

Concept:

To answer this question, we need to recall the concept of inverse trigonometric functions.

• Trigonometric functions are real functions in which angle of a right anhled triangle is related to ratios of two side lengths.
• Inverse trigonometric functions  are also called antitrigonometric functions , are the inverse functions of the trigonometric functions.

Given:

The trigonometric function relation:  $tan^{-1} \frac{1}{x} = cot^{-1} x$.

To Find:

The value of x for which the given relation holds.

Solution:

Let  $tan^{-1}\frac{1}{x}$ = X                  (1)

and $cot^{-1}x$ = Y                   (2)

consider equation (1)

       $tan^{-1}\frac{1}{x}$ = X

                 $\frac{1}{x}$ = tan X

Since, cot X = $\frac{1}{tan X}$              (by property of trigonometric functions)

          cot X = x

                X = $cot^{-1}x$

On comparing with equation (2)

                X = Y

So , the value of x does not depends on the given equation i.e. x can take any value.

Hence, x ∈ $R$ i.e. x belongs to real numbers.