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Let x and y be real numbers such that
sin(x)+sin(y)=a
cos(x)+cos(y)=b
Determine sin(x+y) and cos(x+y).
ON SQUARING AND ADDING BOTH THE EQUATIONS WE GET 1+1+2SINXSINY+2COSXCOSY=a^2+b^2 =2(1+sin(x+y))=a^2+b^2 =sin(x+y)=a^2+b^2-2/2 =similarly cos(x+y)=square root of 1-sin^2(x+y)
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