How do you use the sum to product formulas to write the sum or difference $sin (α + β) - sin (α - β)$ $sin(alpha+beta)-sin(alpha-beta)$ as a product?

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How do you use the sum to product formulas to write the sum or difference $sin (α + β) - sin (α - β)$ $sin(alpha+beta)-sin(alpha-beta)$ as a product?

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Answer 1 · 2017-01-13T13:51:42

The answer is $= 2 cos α sin β$ $=2cosalphasinbeta$

Explanation:

$sin (A \pm B) = sin A cos B \pm cos A sin B$ $sin(A+-B)=sinAcosB+-cosAsinB$

Therefore

$sin (α + β) = sin α cos β + cos α sin β$ $sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta$

$sin (α - β) = sin α cos β - cos α sin β$ $sin(alpha-beta)=sinalphacosbeta-cosalphasinbeta$

$sin (α + β) - sin (α - β) = (sin α cos β + cos α sin β) - (sin α cos β - cos α sin β)$ $sin(alpha+beta)-sin(alpha-beta)=(sinalphacosbeta+cosalphasinbeta)-(sinalphacosbeta-cosalphasinbeta)$

$=cancel(sinalphacosbeta)+cosalphasinbeta-cancel(sinalphacosbeta)+cosalphasinbeta$

$=2cosalphasinbeta$

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How do you use the sum to product formulas to write the sum or difference $sin (α + β) - sin (α - β)$ $sin(alpha+beta)-sin(alpha-beta)$ as a product?

1 Answer

Explanation:

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