Question 415993
given:

{{{sin(arcsinx+ arccosx)}}}

solution:


{{{sin(A+B) = sinAcosB + cosAsinB}}}


{{{sin(arcsin(x)) = x}}}


{{{cos(arcsin(x)) = sqrt(1-x^2)}}}


{{{sin(arccos(x)) = sqrt(1-x^2)}}}


{{{cos(arccos(x)) = x}}}


{{{sin(arcsinx+arccosx)}}}


= {{{sin(arcsin(x))cos(arccos(x)) + cos(arcsin(x))sin(arccos(x))}}}


={{{ x^2 + (1-x^2)}}}


= {{{1}}}