Question

cos-1(\(\frac { 1 }{ 2 }\)) + 2 sin-1(\(\frac { 1 }{ 2 }\))

Answer 1

cos-1(\(\frac { 1 }{ 2 }\)) + 2 sin-1(\(\frac { 1 }{ 2 }\))

Now, cos-1(\(\frac { 1 }{ 2 }\)) = \(\frac { π }{ 3 }\)

and sin-1(\(\frac { 1 }{ 2 }\)) = \(\frac { π }{ 6 }\)

∴ cos-1(\(\frac { 1 }{ 2 }\)) + 2 sin-1(\(\frac { 1 }{ 2 }\))

= \(\frac { π }{ 3 }\) + 2 x \(\frac { π }{ 6 }\) = \(\frac { 2π }{ 3 }\).