定义运算：x*y=x2-y2+2xy，则cosπ3*sinπ3的值是（）A．3−14B．3+12C．−3+12D．3−12

Question

定义运算：x*y=x²-y²+2xy，则cos(π)/(3)*sin(π)/(3)的值是（　　）

A．(√(3)−1)/(4)
B．(√(3)+1)/(2)
C．−(√(3)+1)/(2)
D．(√(3)−1)/(2)

Answer 1

由题意，cos(π)/(3)*sin(π)/(3)=cos²(π)/(3)-sin²(π)/(3)+2cos(π)/(3)sin(π)/(3)=cos(2π)/(3)+sin(2π)/(3)=(√(3)−1)/(2)，故选D．