Question

Write the given expression as an algebraic expression
sin(arctan x- arcsin x)

Answer 1

sin(a-b) = .. ?

Answer 2

\[put arc \tan x=\theta,x=\tan \theta \]
\[arc \sin x=\Phi ,x=\sin \Phi \]

\[\sin \left( \theta-\Phi \right)=\sin \theta \cos \Phi-\cos \theta \sin \Phi \]\[\cos \Phi=\frac{ \sqrt{1-x ^{2}} }{1}=\sqrt{1-x ^{2}}\]
\[\sin \theta=\frac{ x }{\sqrt{1+x ^{2}} },\cos \theta=\frac{ 1 }{ \sqrt{1+x ^{2}} }\]
substitute the values