ntsin(2tan-1(1/3))+ cos (tan-1(2(2)1/2))=n

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c o s^{- 1} (\frac{1}{2}) + t a n^{- 1} (\frac{1}{\sqrt{3}})

{cosec}^{- 1} (3 / 2) + {cos}^{- 1} (2 / 3) - 2 {cot}^{- 1} (1 / 7) - {cot}^{- 1} 7

{cot}^{- 1} 7

{sin}^{- 1} x + {cos}^{- 1} x = π / 2, {tan}^{- 1} x + {cot}^{- 1} x = π / 2, {cosec}^{- 1} x = {sin}^{- 1} (1 / x),

{cot}^{- 1} (1 / x) = {tan}^{- 1} (x), {cot}^{- 1} (x) = {tan}^{- 1} (1 / x)

s i n [2 t a n^{- 1} (\frac{1}{3})] + c o s [t a n^{- 1} (2 \sqrt{2})] =

$t a n^{- 1} (\frac{1}{3}) + t a n^{- 1} (\frac{1}{7}) + . . . . . . . . + t a n^{- 1} (\frac{1}{n^{2} + n + 1}) =$

{sin}^{- 1} \frac{1}{2} + {cos}^{- 1} \frac{1}{2} + {tan}^{- 1} \frac{1}{\sqrt{3}}

(a) \frac{2 π}{3} (b) \frac{π}{2}

(c) \frac{3 π}{4} (d) \frac{5 π}{6}

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