Question

sin(tan^-1 x) mod of x < 1 find x​

Answer 1

tan^-1x=Y

Tan Y=X sec^2Y-Tan^2Y=1

So secY=√(1+tan^2Y)=√(1+X^2)

secY=1/CosY

CosY=1/√(1+XX^2)

Sin Y =√(1-cos^2Y)= (X/√(1+X^2))

TAN^-1X=X/√(1+x^2)/√1+X^2)=

TanY=SinY/CosY

Tan^-1X=Y

Sin(tan^-1X)=SinY=X/(√1+X^2)