Question 969685
{{{ sin(x/2) + cos(x/2) = sqrt( 2 ) }}}
{{{sqrt((1-cosx)/2) +sqrt((1+cosx)/2)  = sqrt( 2 ) }}}
square both sides:
{{{(1-cosx)/2 +2*sqrt((1-cosx)(1+cosx)/4)+(1+cosx)/2  = 2 }}}
{{{(1-cosx)/2 +2*sqrt((1-cos^2(x))/4)+(1+cosx)/2  = 2 }}}
{{{(1-cosx)/2 +2*sqrt((sin^2(x))/4)+(1+cosx)/2  = 2 }}}
{{{(1-cosx)/2 +sinx+(1+cosx)/2  = 2 }}}
sinx+1=2
sinx=1
x=π/2
check:
sin(x/2)+cos)x/2)=√2/2+√2/2=√2