Question

Tan-1 2/11 + tan-1 7/24 = tan-1 ½

Answer 1

Answer:

Step-by-step explanation:

$tan^{-1}\dfrac{2}{11} + tan^{-1}\dfrac{7}{24} =tan^{-1}\dfrac{1}{2}$

$L.H.S.= tan^{-1}\dfrac{2}{11} + tan^{-1}\dfrac{7}{24}\\\\=tan^{-1}(\dfrac{\dfrac{2}{11}+\dfrac{7}{24}  }{1-\dfrac{2}{11}.\dfrac{7}{24}  })$

[  $tan^{-1}x+tan^{-1}y=tan^{-1}(\dfrac{x+y}{1-xy} )$  ]

$=tan^{-1}(\dfrac{48+77}{24*11-14} )\\\\=tan^{-1}(\dfrac{125}{250} )\\\\\\=tan^{-1}(\dfrac{1}{2})=R.H.S.$

L.H.S. = R.H.S.