prove the following result

sin^-1(-4/5)=tan^-1(-4/3)=cos^-1(-3/5) – pi

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