Two slopes leave a port at the same time one goes 24 km/hr in the direction N 45^o E and other travels 32 km/hr in the direction S 75^o E. Find the distance between the ships at the end of 3 hours.

Prove that cos^-1 x = \(2\sin ^{ -1 }{ \sqrt { \frac { 1-x }{ 2 } } } =2\cos ^{ -1 }{ \sqrt { \frac { 1+x }{ 2 } } } \)

Prove \(\frac { cosA }{ a } +\frac { cosB }{ b } +\frac { cosC }{ c } =\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ 2abc } \)

Prove that \(cos\frac { B-C }{ 2 }= \frac { b+c }{ a } sin\frac { A }{ 2 } \)

In ∆ABC, if tan \(\frac{A}{2}=\frac{5}{6}\) and tan \(\frac{C}{2}=\frac{2}{5}\), then show that a, b, c, are in A.P.