Question

sin(tan^-1x-sin^-1x)express algebraically in terms of x please need help with this and please explain each step

Answer 1

you mean
\[\sin (\tan^{-1} x-\sin^{-1} x)\]???

Answer 2

yes that is the sum

Answer 3

\[\sin (\frac{ \sin^{-1} x }{ \cos^{-1} x }- \sin^{-1} x)\]
\[\sin (\frac{ \sin^{-1} x(1- \cos^{-1} x)}{ \cos^{-1} x })\]
\[x(\frac{ 1 }{ \cos^{-1} x }-1)\]
\[x(\sec ^{-1}x-1)\]

Answer 4

can you just explain the third step please

Answer 5

\[\sin*\sin ^{-1}x(\frac{ 1-\cos^{-1} x }{ \cos^{-1} x })\]
now sin and sin inverse cancels out and x remains