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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).

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).

Grade:11

1 Answers

SREEDHAR P
15 Points
9 years ago

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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