Question

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Answer 1

$\huge{\mathcal{\underline{\green{SOLUTION}}}}$

Here we take only principal value of

${cos}^{ - 1} x \: \: \: and \: \: {tan}^{ - 1} x$

The given Expression =

${tan}^{ - 1} [ \: 2 {sin} (2 {cos}^{ - 1} \frac{ \sqrt{3} }{2}) ]$

$= {tan}^{ - 1} [ \: 2 {sin} (2 \times \frac{\pi}{6} ) ]$

$= {tan}^{ - 1} [ \: 2 {sin} \frac{\pi}{3} ]$

$= {tan}^{ - 1} [ \: 2 \times \frac{ \sqrt{3} }{2} ]$

$= {tan}^{ - 1} [ \ \sqrt{3} \: ]$

$= \frac{\pi}{3}$

Answer 2

Answer:

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