Answer
452.7k+ views
Hint: To solve this problem we need to have basic knowledge about trigonometric and its values, and also basic calculation for simplifying the values.
Complete step-by-step answer:
Given ${\tan ^{ - 1}}\sqrt 3 + {\cot ^{ - 1}}x = \dfrac{\pi }{2} - - - - - - - > (1)$
We know that ${\tan ^{ - 1}}\sqrt 3 = \dfrac{\pi }{3}$
On substituting the above value in equation (1), we get
$ \Rightarrow \dfrac{\pi }{3} + {\cot ^{ - 1}}x = \dfrac{\pi }{2}$
$ \Rightarrow {\cot ^{ - 1}}x = \dfrac{\pi }{2} - \dfrac{\pi }{3}$
On taking L.C.M we can rewrite the above term as
$
\Rightarrow {\cot ^{ - 1}}x = \dfrac{{3\pi - 2\pi }}{6} \\
\Rightarrow {\cot ^{ - 1}}x = \dfrac{\pi }{6} \\
$
$
\Rightarrow x = \cot \dfrac{\pi }{6} = \sqrt 3 \\
\Rightarrow x = \sqrt 3 \\
$
Therefore the value of $x = \sqrt 3 $.
Note: In this problem we took the ${\tan ^{ - 1}}\sqrt 3 $ value and replaced it in the equation. Later we have simplified the $\pi$ values which is equal to cot inverse x and on further simplification we got x value. In this kind of problem instead of solving the equation it’s better to find the value of the term and simplify.
Complete step-by-step answer:
Given ${\tan ^{ - 1}}\sqrt 3 + {\cot ^{ - 1}}x = \dfrac{\pi }{2} - - - - - - - > (1)$
We know that ${\tan ^{ - 1}}\sqrt 3 = \dfrac{\pi }{3}$
On substituting the above value in equation (1), we get
$ \Rightarrow \dfrac{\pi }{3} + {\cot ^{ - 1}}x = \dfrac{\pi }{2}$
$ \Rightarrow {\cot ^{ - 1}}x = \dfrac{\pi }{2} - \dfrac{\pi }{3}$
On taking L.C.M we can rewrite the above term as
$
\Rightarrow {\cot ^{ - 1}}x = \dfrac{{3\pi - 2\pi }}{6} \\
\Rightarrow {\cot ^{ - 1}}x = \dfrac{\pi }{6} \\
$
$
\Rightarrow x = \cot \dfrac{\pi }{6} = \sqrt 3 \\
\Rightarrow x = \sqrt 3 \\
$
Therefore the value of $x = \sqrt 3 $.
Note: In this problem we took the ${\tan ^{ - 1}}\sqrt 3 $ value and replaced it in the equation. Later we have simplified the $\pi$ values which is equal to cot inverse x and on further simplification we got x value. In this kind of problem instead of solving the equation it’s better to find the value of the term and simplify.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)