How do you find the exact value of sin(tan^-1 -5/7)sin(tan−1−57)?

1 Answer
A. S. Adikesavan
Jan 13, 2017

-5/sqrt74−5√74

Explanation:

tan^(-1)(-5/7)= sin^(-1)(-5/sqrt(5^2+7^2))=sin^(-1)(-5/sqrt74)tan−1(−57)=sin−1(−5√52+72)=sin−1(−5√74)

The given expression is

sin(sin^(-1)(-5/sqrt74))=-5/sqrt74sin(sin−1(−5√74))=−5√74.

Note that , if arc tan is negative, the angle is in Q_4Q4, and so,

arc sin in Q_4arcsin∈Q4 is also negative.

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