tanAtanB =square root of(a-b)/(a+b),prove that(a-bcos2A)(a--bcos2B)=a^2-b^2

Dear Aditya,

Another commonly-used set of formulae allows us to turn a product of sines and cosines into a sum or difference of sines and cosines. Here they are:

sin(A)+sin(B)=2sin{(A+B)/2}cos{(A-B)/2}

sin(A)-sin(B)=2cos{(A+B)/2}sin{(A-B)/2}

cos(A)+cos(B)=2cos{(A+B)/2}cos{(A-B)/2}

cos(A)-cos(B)=-2sin{(A+B)/2}sin{(A-B)/2}.

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