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sin(α)cos(β) – formula’s demonstration

Posted in Math Theory by Lia on 03/24/2013

For a list with trigonometric identities click here

 

We start from the known formulas:

 [1]   sin({alpha} + {beta}) = sin{alpha}cos{beta} + cos{alpha}sin{beta}  (look for  sin({alpha} + {beta})‘s demonstration  here)

and

 [2]  sin({alpha} - {beta}) = sin{alpha}cos{beta} - cos{alpha}sin{beta}   (look for  sin({alpha} - {beta})‘s demonstration  here)

If we add [1] and [2] we have:

sin({alpha} + {beta}) + sin({alpha} - {beta}) = sin{alpha}cos{beta} + cos{alpha}sin{beta} + sin{alpha}cos{beta} - cos{alpha}sin{beta}   {}{right}{} 

sin({alpha} + {beta}) + sin({alpha} - {beta}) = {2}sin{alpha}cos{beta}

↓↓

sin{alpha}cos{beta} = {{sin({alpha} + {beta}) + sin({alpha} - {beta})}/2}

 

 

 

 

 

 

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