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Question
The principal value of sin−1tan(−5π4) is
The principal value of sin−1tan(−5π4) is
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Solution
The correct option is D - π/2
sin−1{tan(−5π4)}
=sin−1{−tan(π+π4)}
=sin−1(−tanπ4)
=−sin−1(1)=−sin−1(sinπ2)
=−π2
sin−1{tan(−5π4)}
=sin−1{−tan(π+π4)}
=sin−1(−tanπ4)
=−sin−1(1)=−sin−1(sinπ2)
=−π2
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