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sin(a+b)*cos(a-b)=1,求sina+cosb
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∵sin(a+b)=sina·cosb+sinb·cosa
cos(a-b)=cosa·cosb+sina·sinb
∴sin(a+b)·cos(a-b)=(sina·cosb+sinb·cosa)·(cosa·cosb+sina·sinb)=1
sina·cosa·(cos^2 b +sin^2 b) +sinb·cosb·(sin^2 a +cos^2 a)=1
∴sina·cosa+sinb·cosb=1
cos(a-b)=cosa·cosb+sina·sinb
∴sin(a+b)·cos(a-b)=(sina·cosb+sinb·cosa)·(cosa·cosb+sina·sinb)=1
sina·cosa·(cos^2 b +sin^2 b) +sinb·cosb·(sin^2 a +cos^2 a)=1
∴sina·cosa+sinb·cosb=1
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