Prove that, tan^-1(1/2)+tan^-1(1/3)=π/4

 

Prove that, tan^-1(1/2)+tan^-1(1/3)=π/4
Prove that, tan^-1(1/2)+tan^-1(1/3)=π/4

Questions:Prove that,tan^-1(1/2)+tan^-(1/3)=π/4



L.H.S=\(tan^{-1} \frac{1}{2}+tan^{-1}\frac{1}{3}\)

         =\(tan^{-1}\frac{½+⅓}{1-½*⅓}\)

         =\(tan^{-1}\frac{\frac{3+2}{6}}{\frac{6-1}{6}}\)

         =\(tan^{-1}\frac{5/6}{5/6}\)

         =\(tan^{-1}1\)

        =\(\frac{π}{4}\)

        =R.H.S. [proved]
 
L.H.S=tan^-1{(1/2)+tan^-1(1/3),

          =tan^-1{((1/2+1/3)/(1-1/2*1/3)}

           =tan^-1{(5/6)/(5/6)}

           =tan^-1(1)

           =π/4

           =R.H.S. [proved]


L.H.S=arctan(1/2)+arctan(1/3)
    
          =arctan{(1/2+1/3)/(1-1/2*1/3)}
 
          =arcta{(5/6)/(5/7)}
 
          =arctan(1)
          
           = π/6
          
           =R.H.S [proved]

Description

Line1:We put our mathematical problem.

Line2: we use a trigonometric formula .

After that: we complete some algebraic calculation.

Before last line:we put the value of arctan(1)


  












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