Product to Sum Formulas sin α sin β 2 1 = [cos (α – β)

Product to Sum Formulas sin α sin β 2 1 = [cos (α – β) – cos (α + β ...

2. 1. = [sin (α + β) + sin (α – β)]. Proof: Equation 1 cos (α – β) = cos α cos β + sinα sin β cos (α + β) = cos α cos β – sinα sin β cos (α – β) – cos (α + β)= 2 sinα sin β.

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Product to Sum Formulas

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sin ! sin " =

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2

Proof: Equation 1 cos (! – ") = cos ! cos " + sin ! sin " cos (! + ") = cos ! cos " – sin ! sin " cos (! – ") – cos (! + ") = 2 sin ! sin " 1 [cos (! – ") – cos (! + ")] = sin ! sin " 2

sin ! sin " =

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2

Proof: Equation 2 cos (! – ") = cos ! cos " + sin ! sin " cos (! + ") = cos ! cos " – sin ! sin " cos (! – ") + cos (! + ") = 2 cos ! cos " 1 [cos (! – ") + cos (! + ")] = cos ! cos " 2

sin ! sin " =

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2

Proof: Equation 3 sin (! + ") = sin ! cos " + cos ! sin " sin (! – ") = sin ! cos " – cos ! sin " sin (! + ") + sin (! – ") = 2 sin ! cos " 1 [sin (! + ") + sin (! – ")] = sin ! cos " 2

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2 Evaluate the following sin ! sin " =

sin (7#) sin (4#)

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1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2 Evaluate the following sin ! sin " =

cos (5#) cos (2#)

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2 Evaluate the following sin ! sin " =

sin (6#) cos (#)

© iTutoring.com Product to Sum Formulas Pg. 3

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2 Evaluate the following sin ! sin " =

cos (2#) cos (7#)

1 1 [cos (! – ") – cos (! + ")] cos ! cos " = [cos (! – ") + cos (! + ")] 2 2 1 sin ! cos " = [sin (! + ") + sin (! – ")] 2 Evaluate the following sin ! sin " =

sin (3#) cos (9#)

© iTutoring.com Product to Sum Formulas Pg. 4