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Question

Solve:sin1(1x21+x2)

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Solution

Consider the given function =sin1(1x21+x2)

Let, put x=tanA then A=tan1x ……. (1)

Then,

sin1(1tan2A1+tan2A)

=sin1⎜ ⎜ ⎜ ⎜1sin2Acos2A1+sin2Acos2A⎟ ⎟ ⎟ ⎟

=sin1(cos2Asin2Acos2A+sin2A)

=sin1(cos2A1)

=sin1cos2A

=sin1sin(9002A)

=9002A

By equation (1) and we get,

=9002tan1x

Hence, this is the answer.


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