Prove that \(\cos x\cos \left( \frac { \pi }{ 3 } -x \right) cos\left( \frac { \pi }{ 3 } +x \right)=\frac14 cos3x\)

The minute hand of a watch is 1.5 cm long. How far does its top move in 40 minutes?

Prove that \(\cos { 5x } =16\cos ^{ 5 }{ x } -20\cos ^{ 3 }{ x } +5\cos { x } \)

If the sides of a \(\triangle\)ABC are a = 4, b = 6, and c = 8, show that \(4\cos { B } +3\cos { C } =2\)

Solve: tan^-1 (x + 1) + tan^-1 (x - 1) = tan^-1\(\frac{4}{7}\).0