Question

2tan-1 1/2 + tan-1 1/7 = tan-1 31 / 17

Answer 1

Answer:

2tan−11/2+tan−11/7=tan−131/17Read more on Sarthaks.com - https://www.sarthaks.com/20163/prove-that-2tan-1-1-2-tan-1-1-7-tan-1-31-17

Answer 2

Answer:

Step-by-step explanation:

$2tan^{-1}\dfrac{1}{2} +tan^{-1}\dfrac{1}{7} =tan^{-1}\dfrac{31}{17}$

$L.H.S.=2tan^{-1}(\dfrac{1}{2} )+tan^{-1}(\dfrac{1}{7} )\\\\\\=tan^{-1}(\dfrac{2*\dfrac{1}{2} }{1-(\dfrac{1}{2})^2 } )+tan^{-1}(\dfrac{1}{7} )\\\\\\(2tan^{-1}x=tan^{-1}\dfrac{2x}{1-x^2} ;|x|<1)\\\\\\=tan^{-1}\dfrac{4}{3} +tan^{-1}(\dfrac{1}{7} )\\\\\\=tan^{-1}(\dfrac{\dfrac{4}{3}+\dfrac{1}{7}  }{1-\dfrac{4}{3}.\dfrac{1}{7}  } )\\\\\\(tan^{-1}x+tan^{-1}y=tan^{-1}(\dfrac{x+y}{1-xy} ))\\\\\\=tan^{-1}(\dfrac{7*4+3*1}{21-4} )\\\\\\=tan^{-1}(\dfrac{31}{17} )=R.H.S.$