求证sin(a+b)sin(a-b)=sina^2-cosb^2

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证明：sin(a+b)sin(a-b)
=(sinacosb+cosasinb)(sinacosb-cosasinb)
=(sinacosb)^2-(cosasinb)^2
=(cosb)^2[1-(cosa)^2]-(cosa)^2[1-(cosb)^2]
=(cosb)^2-(cosb)^2(cosa)^2-(cosa)^2+(cosa)^2(cosb)^2
=(cosb)^2-(cosa)^2
=(cosb)^2-[1-(sina)^2]
=(sina)^2+(cosb)^2-1
=(sina)^2-(sinb)^2
题目有问题,请楼主认真核对!
======以下答案可供参考======
供参考答案1:
sin(a+b)sin(a-b)=(-1/2)(cos2a-cos2b)
=(-1/2)(1-2sin²a+2cos²b-1)
=sin²a-cos²b