已知sin(pai/4+2a)sin(pai/4-2a)=1/2,求2sin^2a+3cos2a+1的值
问题描述：
已知sin(pai/4+2a)sin(pai/4-2a)=1/2,求2sin^2a+3cos2a+1的值
答
∵sin(π/4+2a)sin(π/4-2a)=1/2∴2sin(π/4+2a)sin(π/4-2a)=1根据积化和差公式2sinAsinB=-cos(A+B)+cos(A-B)-cos[(π/4+2a)+(π/4-2a)]+cos[(π/4+2a)-(π/4-2a)] = 1-cos(π/2)+cos(4a) = 10+cos(4a) = 1cos(4a) ...