Write the value of tan^-1{2 sin(2 cos^-1 √3/2)}.

Question

Write the value of tan^-1{2 sin(2 cos^-1 \(\frac{\sqrt3}2\))}.

Answer 1

Given tan^-1 {2 sin (2 cos^-1 √3/2)}

= tan^-1 {2 sin (2 cos^-1 cos π/6)}

= tan^-1 {2 sin (2 × π/6)}

= tan^-1 {2 sin (π/3)}

= tan^-1 {2 × √3/2}

= tan^-1 {√3}

= π/3

∴ tan^-1 {2 sin (2 cos^-1 √3/2)} = π/3