The required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny
To answer the question, we need to know what trigonometric identities are
<h3>What are trigonometric identities?</h3>
Trigonometric identities are relationships between the trigonometic ratios.
Since we require cosxsiny
Given that
- sin(x + y) = sinxcosy + cosxsiny and
- sin(x - y) = sinxcosy - cosxsiny
So, subtracting both expressions, we have
sin(x + y) - sin(x - y) = sinxcosy + cosxsiny - (sinxcosy - cosxsiny)
= sinxcosy + cosxsiny - sinxcosy + cosxsiny
= sinxcosy - sinxcosy + cosxsiny + cosxsiny
= 0 + 2cosxsiny
= 2cosxsiny
sin(x + y) - sin(x - y) = 2cosxsiny
Dividing through by 2, we have
1/2[sin(x + y) - sin(x - y)] = cosxsiny
So, the required trigonometric identity is 1/2[sin(x + y) - sin(x - y)] = cosxsiny
Learn more about trigonometric identities here:
brainly.com/question/26609988
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