Show that tan−1112 +tan−1247 =tan−121

tan−1x+tan−1y=tan−1(1−xyx+y)tan−1112+tan−1247=tan−1(1−112×247112+247)=tan−1(11×24264−1411×2448+77)=tan−1(250125)=tan−121=RHSHence Proved

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Show that ^{ -1 }{ { 2 }{ 11 } } + ^{ -1 }{ { 7 }{ 24 } }

Question

Show that $tan^{- 1} \frac{2}{11} + tan^{- 1} \frac{7}{24} = tan^{- 1} \frac{1}{2}$

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Show that

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

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13 mins ago

tan^{- 1} x + tan^{- 1} y = tan^{- 1} (\frac{x + y}{1 - x y})

tan^{- 1} \frac{2}{11} + tan^{- 1} \frac{7}{24} = tan^{- 1} (\frac{\frac{2}{11} + \frac{7}{24}}{1 - \frac{2}{11} \times \frac{7}{24}}) = tan^{- 1} (\frac{\frac{48 + 77}{11 \times 24}}{\frac{264 - 14}{11 \times 24}}) = tan^{- 1} (\frac{125}{250}) = tan^{- 1} \frac{1}{2} = R H S

Hence Proved

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Question Text	Show that $tan^{- 1} \frac{2}{11} + tan^{- 1} \frac{7}{24} = tan^{- 1} \frac{1}{2}$
Answer Type	Text solution:1
Upvotes	150