Question 949440

{{{sin(x+40)+sin(x+50)=0}}}

{{{sin(40) cos(x)+cos(40) sin(x) +sin(50) cos(x)+cos(50) sin(x)=0}}}

{{{0.642787cos(x)+0.766 sin(x) +0.766 cos(x)+0.642787 sin(x)=0}}}

{{{0.642787cos(x)+0.766 cos(x)+0.766 sin(x) +0.642787 sin(x)=0}}}

{{{1.408787cos(x)+1.408787 sin(x)=0}}}

{{{1.408787cos(x)/1.408787+1.408787 sin(x)/1.408787=0/1.408787}}}

{{{cos(x)+ sin(x)=0}}}


{{{x = pi*n-pi/4}}},  for all {{{ n}}} element {{{Z}}} ->  often used to denote the set of all integers ({{{Z}}} standing for the German word Zahlen which means "numbers" )

check for these values:
if
{{{n=-1}}} , then {{{x = -pi*1-pi/4}}}=> {{{x = -5pi/4}}}
{{{n=0}}} , then {{{x = pi*0-pi/4}}}=> {{{x = -pi/4}}}
{{{n=1}}} , then {{{x = pi*1-pi/4}}}=> {{{x = 3pi/4}}}....and so on