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prove the following result sin^-1(-4/5)=tan^-1(-4/3)=cos^-1(-3/5) – pi

prove the following result
sin^-1(-4/5)=tan^-1(-4/3)=cos^-1(-3/5) – pi

Grade:12

1 Answers

Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
9 years ago
I'm writing sin^-1(x) as arcsin(x)
arcsin(-x)=-arcsin(x)
arctan(-x)=-arctan(x)
arccos(-x)=pi-arccos(x)
so arcsin(-4/5)=-arcsin(4/5)=A (say)
so sinA=-4/5 =>cosA=3/5=>tanA=-4/3 {because arcsin is defined in first two quadrants and cosine is positive in both} so A=-arctan(4/3)=arctan(-4/3) cos(pi+A)=-cos(A)=-3/5
pi+A=arccos(-3/5) =>A=arccos(-3/5)-pi


Sher Mohammad
faculty askiitians

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