Question 170167
Note: {{{sin(45)=sqrt(2)/2}}}, {{{sin(60)=sqrt(3)/2}}}, {{{sin(90)=1}}}, {{{cos(45)=sqrt(2)/2}}}, {{{cos(60)=1/2}}}, and {{{cos(90)=0}}}



{{{sin(135)=sin(90+45)=sin(90)cos(45)+cos(90)sin(45)=(1)(sqrt(2)/2)+(0)+(sqrt(2)/2)=sqrt(2)/2+0=sqrt(2)/2}}}



So {{{sin(135)=sqrt(2)/2}}}




{{{cos(150)=cos(90+60)=cos(90)cos(60)-sin(90)sin(60)=(0)(1/2)-(1)(sqrt(3)/2)=0-sqrt(3)/2=-sqrt(3)/2}}}



So {{{cos(150)=-sqrt(3)/2}}}




This means that 



{{{sin(135)+cos(150)=sqrt(2)/2+(-sqrt(3)/2)=(sqrt(2)-sqrt(3))/2}}}




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Answer:



So {{{sin(135)+cos(150)=(sqrt(2)-sqrt(3))/2}}}