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tan (2tan inverse X + cot inverse X) at X=2Find the value,I couldn`t understand the X=2 thing

Aashi , 6 Years ago
Grade 12
anser 1 Answers
Arun

Last Activity: 6 Years ago

The question is that we have to find the value of tan( 2tan-1x + cot-1x ) at x = 2.
So, we can rewrite the question as :
tan( tan-1x + tan-1x + cot-1x )
Since we know that tan-1x + cot-1x =  \frac{\pi }{2}  
Therefore, the question now becomes :
         tan(  \frac{\pi }{2}   + tan-1x ) 
If you see this looks like tan( a + b ) formula , where a = \frac{\pi }{2} and b = tan-1x
Therefore, solving using the formula above we will get,
 
\frac{tan(\frac{\pi }{2}) + tan(tan^{-1}x)}{1- tan(\frac{\pi }{2})tan(tan^{-1}x)}
 
\frac{\infty + x }{1 - (\infty )(x)}  
 
= 0 
 
This is your answer.
 Hope this will help you ! 

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