Question

sin(x+2y)cos(x-2y)=sin2x+sin4x证明？

谢谢!

Answer 1

你的等式是错的，右边少了1/2，不是sin4x，而是sin4y。

Answer 2

sin(A+B)=sinA.cosB+cosA.sinB (1)
sin(A-B)=sinA.cosB-cosA.sinB (2)
(1)+(2)
sin(A+B)+sin(A-B)= 2sinA.cosB
x+2y = A (3)
x-2y =B (4)
(3)+(4)
A+B= 2x
(3)-(4)
A-B = 4y
ie
sin(A+B)+sin(A-B)= 2sinA.cosB
sin(2x)+sin(4y)= 2sin(x+2y).cos(x-2y)