Given 0 x 12 then the value of tan ⁡( sin^-1 ⁡( x 2+ 1-x^2 2)- sin^-1 ⁡x) is

Question

Accepted Answer

Correct answer: A. (a) Let, y= tan( sin^-1( x 2+ 1-x^2 2)- sin^-1x) Put x= sin ⁡ , we get y= tan( sin^-1( sin 2+ 1- sin^2 2)- sin^-1 ( sin )) = tan( sin^-1 ( sin + cos 2 )- ) = tan( sin^-1( sin cos 4+ cos sin 4)- ) = tan( sin^-1 ( sin( + 4) )- ) = tan ⁡( + 4- )= tan ⁡ 4=1

$Given 0 \leq x \leq \frac{1}{2} then the value of tan (sin^{- 1} (\frac{x}{2} + \frac{1 - x ^{2}}{2}) - sin^{- 1} x) is$

Solution

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