\operatorname { sin } ^ { - 1 } \frac { 3 } { 5 } + \operatorname { co

1.	\operatorname { sin } ^ { - 1 } \frac { 3 } { 5 } + \operatorname { cos } ^ { - 1 } \frac { 15 } { 17 } + \operatorname { sin } ^ { - 1 } \frac { 36 } { 85 } = \frac { \pi } { 2 }
Answer» sin^-1(3/5) + sin^-1(36/85) = π/2- cos^-1(15/17) => sin^-1(3/5√1-(36/85)² + 36/85√1-(3/5)²) = π/2 - cos^-1(15/17) => sin^-1(3/577/85 + 36/854/5) = sin^-1(15/17)=> sin^-1(375/425) = sin^-1(15/17)=> sin^-1(15/17) = sin^-1(15/17) => L.H.S = R.H.S

\operatorname { sin } ^ { - 1 } \frac { 3 } { 5 } + \operatorname { cos } ^ { - 1 } \frac { 15 } { 17 } + \operatorname { sin } ^ { - 1 } \frac { 36 } { 85 } = \frac { \pi } { 2 }

Answer»

sin^-1(3/5) + sin^-1(36/85) = π/2- cos^-1(15/17)

=> sin^-1(3/5*√1-(36/85)² + 36/85*√1-(3/5)²) = π/2 - cos^-1(15/17)

=> sin^-1(3/5*77/85 + 36/85*4/5) = sin^-1(15/17)=> sin^-1(375/425) = sin^-1(15/17)=> sin^-1(15/17) = sin^-1(15/17) => L.H.S = R.H.S