Question

if tan^-1x=pi/10 find cot^-1x

Answer 1

Tan^-1x+Cot^-1x=π/2 (Identity)
So cot^-1x=π/2-π/10=2π/5
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Answer 2

Answer:

$\frac{2\pi }{5}$ is the required value of $cot^-1x$ .

Step-by-step explanation:

Explanation:

Given , $tan^-1x = \frac{\pi }{10}$

As we know that , $tan^-1x + cot^-1x = \frac{\pi }{2}$

Step 1:

We have the value of $tan^-1x = \frac{\pi }{10}$  .

Now , put the value of  $tan^-1x = \frac{\pi }{10}$  in the trigonometry formula ,

$tan^-1x + cot^-1x = \frac{\pi }{2}$ we get ,

⇒$\frac{\pi }{10} + cot^-1x = \frac{\pi }{2}$

⇒$cot ^-1x = - \frac{\pi }{10 } + \frac{\pi }{2}$

⇒ $cot ^-1x = \frac{-\pi + 5\pi }{10}$ = $\frac{2\pi }{5}$

Final answer :

Hence , the value of $cot ^-1x \ is \frac{2\pi }{5}$ .

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