CALCULUS SYMPLIFYNG EXPRESSIONS

Question

Simplify the expression    

 

sin( tan^-1 x)

Answer 1

sin(tan^-1x)

tan^-1x means tan of what angle equals x

call the angle θ

tanθ=x

construct a right triangle

tan=opposite/adjacent

tanθ=x=x/1

opposite=x

adjacent=1

hypotenuse=√(x²+1)

sin=opposite/hypotenuse

sinθ=x/√(x²+1)

therefore...

sin(tan-1x)=x/√(x²+1)