3. What is the value of sin inverse 5/13

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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

Prove

(a)

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

(b)

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

(c)

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

$Find the reciprocal (multiplicative inverse) of : (i) \frac{3}{5} \times \frac{2}{3} (i i) \frac{- 8}{3} \times \frac{13}{- 7} (i i i) \frac{- 3}{5} \times \frac{- 1}{13}$

Q. Find the multiplicative inverse of the following:

- 13

- \frac{13}{19}

and

- \frac{5}{8} \times - \frac{3}{7}

The value of $cos ({sin}^{- 1} \frac{3}{5} + {sin}^{- 1} \frac{5}{13})$ is ____

Q. The value of

{sin}^{- 1} (\frac{12}{13}) - {sin}^{- 1} (\frac{3}{5})

is equal to :

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