Question

cot inverse 2+ cot inverse 3

Answer 1

this is required answer

Answer 2

Answer:

The value of given expression $cot^{-1} (2)+cot^{-1} (3)$ is $45^0$ or pi/4 radians.

Step-by-step explanation:

We are given an trigonometric expression $cot^{-1} (2)+cot^{-1} (3)$

We are asked to find the value of the given expression.

Let us write the given expression in terms of tan

$cot^{-1} (2)$

Therefore it can be written as $tan^{-1} (\frac{1}{2} )$

similarly $cot^{-1} (3)$

It can be written as $tan^{-1} (\frac{1}{3} )$

Now, write the given expression in terms of tan

$tan^{-1} (\frac{1}{2} )+tan^{-1} (\frac{1}{3} )$

We can simplify this by using the inverse trigonometric formulae.

$tan^{-1} (x)+tan^{-1} (y)=tan^{-1} (\frac{x+y}{1-xy} )$

$tan^{-1} (\frac{\frac{1}{2} +\frac{1}{3} }{1-\frac{1}{2}\frac{1}{3} } )$

On simplification. We get,

$tan^{-1} (\frac{5}{5})$

$tan^{-1} (1)$

$45^0$ or pi/4 radians.

Therefore, the value of $cot^{-1} (2)+cot^{-1} (3)$  is $45^0$ or pi/4 radians.