2 π-( sin -1 (4/5)+ sin -1 (5/13)+ sin -1 (16/65)) is equal to:

Question

2 π-( sin -1 (4/5)+ sin -1 (5/13)+ sin -1 (16/65)) is equal to: (A) (7 π/4) (B) (5 π/4) (C) (3 π/2) (D) (π/2)

Tardigrade Admin · Accepted Answer

2 π-( sin -1((4/5))+ sin -1((5/13))+ sin -1((16/65))) =2 π-( tan -1((4/3))+ tan -1((5/12))+ tan -1((16/63))) =2 π-( tan -1((63/16))+ tan -1((16/63))) =2 π-(π/2)=(3 π/2)

Q. $2 π - (sin^{- 1} \frac{4}{5} + sin^{- 1} \frac{5}{13} + sin^{- 1} \frac{16}{65})$ is equal to:

$\frac{7 π}{4}$

$\frac{5 π}{4}$

$\frac{3 π}{2}$

$\frac{π}{2}$

$2 π - (sin^{- 1} (\frac{4}{5}) + sin^{- 1} (\frac{5}{13}) + sin^{- 1} (\frac{16}{65}))$
$= 2 π - (tan^{- 1} (\frac{4}{3}) + tan^{- 1} (\frac{5}{12}) + tan^{- 1} (\frac{16}{63}))$
$= 2 π - (tan^{- 1} (\frac{63}{16}) + tan^{- 1} (\frac{16}{63}))$
$= 2 π - \frac{π}{2} = \frac{3 π}{2}$

Q. 2π−(sin−154​+sin−1135​+sin−16516​) is equal to:

47π​

45π​

23π​

2π​