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Property 4

43.The value ...

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43.The value of sin inverse (5/13) + cot inverse (3/4) is equal to (1) sin inverse (63/65) (2) sin inverse (12/13) (3) sin inverse (65/68) (4) sin inverse (5/12)

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Inverse circular functions,Principal values of

{s i n}^{- 1} x, {c o s}^{- 1} x, {t a n}^{- 1} x

{t a n}^{- 1} x + {t a n}^{- 1} y = {t a n}^{- 1} \frac{x + y}{1 - x y}

x y < 1

π + {t a n}^{- 1} \frac{x + y}{1 - x y}

x y > 1

{s i n}^{- 1} \frac{4}{5} + {s i n}^{- 1} \frac{5}{13} + {s i n}^{- 1} \frac{16}{65} = \frac{π}{2}

{s i n}^{- 1} \frac{3}{5} + {s i n}^{- 1} \frac{8}{17} = {c o s}^{- 1} \frac{36}{85}

{s i n}^{- 1} \frac{3}{5} + {c o s}^{- 1} \frac{12}{13} = {c o s}^{- 1} \frac{33}{65}

{cos}^{- 1} (cos (- 5)) + {sin}^{- 1} (sin (6)) - {tan}^{- 1} (tan (12))

is equal to
(The inverse trigonometric functions take the principal values)

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