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Question

Find the value of tan1[2cos(2sin112)].

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Solution

Let y=sin1(12)
siny=12
siny=sin(π6)
Range of principal value of sin1 is [π2,π2]
y=π6
Now,
tan1[2cos(2sin112)]=tan1[2cos(2×π6)]
tan1[2cos(2sin112)]=tan1[2cosπ3]
tan1[2cos(2sin112)]=tan1[2×12]
tan1[2cos(2sin112)]=tan1[1]
tan1[2cos(2sin112)]=tan1[tanπ4]
tan1[2cos(2sin112)]=π4

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