Question

Subtract the sum and difference identities for sin x to derive 1/2 [sin(x+y)+sin(x-y)]= cos x sin y

Answer 1

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

What are trigonometric identities?

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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