1.

What is the examples of the formula sin(a+b) = sina×cosb+cosa×sinb​

Answer»

Here are two for the PRICE of one (using Euler's formula):

COS(A+B)+ISIN(A+B)≡ei(A+B)≡eiA×eiB

cos⁡(A+B)+isin⁡(A+B)≡ei(A+B)≡eiA×eiB

≡[cos(A)+isin(A)][cos(B)+isin(B)]

≡[cos⁡(A)+isin⁡(A)][cos⁡(B)+isin⁡(B)]

≡[cos(A)cos(B)−sin(A)sin(B)]+i[sin(A)cos(B)+cos(A)sin(B)]

≡[cos⁡(A)cos⁡(B)−sin⁡(A)sin⁡(B)]+i[sin⁡(A)cos⁡(B)+cos⁡(A)sin⁡(B)]

Now equate imaginary parts to give the RESULT for sin(A+B)sin⁡(A+B) (and, if you want, equate real parts to give the result for cos(A+B)cos⁡(A+B)).


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