Question

tan inverse[2cos(2sin inverse 1/2)]​

Answer 1

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Actually Welcome to the Concept of the Inverse trigonometry.

Now basically we know that, in the inverse trigonometry, the angle should lie in the respective principle chain to get the correct answer.

Such that,

For the following ratios, the principle chain are,

Sin => (-π/2,π/2)

Cos => (0,π)

tan => (-π/2,π/2)

so now here,

=> tan^-1 (2 cos ( 2 sin^-1( 1/2) ))

so we get as,

⭐tan^-1 (1)

= π/4