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प्रश्न
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
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उत्तर
Let `sin^-1 1/2 = x`.
Then, `sin x = 1/2 = sin (pi/6)`.
∴ `sin^-1 1/2 = pi/6`
∴ `tan^-1 [2 cos (2 sin^-1 1/2)]`
= `tan^-1 [2 cos (2 xx pi/6)]`
= `tan^-1 [2 cos pi/3]`
= `tan^-1 [2 xx 1/2]`
= tan−1 1
= `pi/4`
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