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| 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)