How to use the product-to-sum formula to write the product as a sum or difference? 4 cos pi/3 sin 5pi/6

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1 Answer
Jim G.
Jan 31, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"product to sum/difference formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(2cosAsinB=sin(A+B)-sin(A-B))color(white)(2/2)|)))#

#"here "A=pi/3" and "B=(5pi)/6#

#rArr4cos(pi/3)sin((5pi)/6)#

#=2[sin(pi/3+(5pi)/6)-sin(pi/3-(5pi)/6)]#

#=2[sin((7pi)/6)-sin(-pi/2)]#

#=2[-sin(pi/6)-sin(-pi/2)]#

#=2(-1/2+1)#

#=2xx1/2=1#

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