SOLUTION: Write the expression as a sum or difference of trigonometric functions: 2sin(35)cos(84)

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Question 1025685: Write the expression as a sum or difference of trigonometric functions:
2sin(35)cos(84)
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write the expression as a sum or difference of trigonometric functions:
2sin(35)cos(84)
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x+y = 84
x-y = 35
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2x = 119
x = 59.5
y = 24.5
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Ans:: 2sin(59.5-24.5)cos(59.5+24.5)
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Cheers,
Stan H.
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Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor doesn't understand. Here's what you want:
2sin(35°)cos(84°)

 sin(35°+84°) = sin(35°)cos(84°)+cos(35°)sin(84°)
 sin(35°-84°) = sin(35°)cos(84°)-cos(35°)sin(84°)

Simplify the left sides:

sin(35°+84°)= sin(119°) = sin(180°-61°) = sin(61°)
sin(35°-84°)= sin(-49°) = -sin(49°) 

         sin(61°) =  sin(35°)cos(84°)+cos(35°)sin(84°)
        -sin(49°) =  sin(35°)cos(84°)-cos(35°)sin(84°)
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sin(61°)-sin(49°) = 2sin(35°)cos(84°) 

The right side is what we were given:

Answer: sin(61°)-sin(49°)

Edwin