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prove the following resultsin^-1(-4/5)=tan^-1(-4/3)=cos^-1(-3/5) – pi
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)=-3/5pi+A=arccos(-3/5) =>A=arccos(-3/5)-piSher Mohammadfaculty askiitians
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