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Y_Kistochka [10]
3 years ago
9

Sin(x-y)+sin(x-y prove the identity

Mathematics
1 answer:
Nikitich [7]3 years ago
7 0

Step-by-step explanation:

\sin(x - y)  +  \sin(x + y)  = 2 \sin(x)  \cos(y)

We use the sum and difference identities.

Remeber the sum difference identity is

\sin(x + y)  =  \sin(x)  \cos(y)  +  \cos( x )  \sin(y)

and

\sin(x - y)  =  \sin(x)  \cos(y)  -  \sin(x)  \cos(y)

So we get

(\sin(x)  \cos(y)  -  \sin(y)  \cos(x) ) +  \sin(x)  \cos(y)  +  \sin(y)  \cos(x)

Combine like Terms.

2 \sin(x)  \cos(y)  = 2 \sin(x)  \cos(y)

We have provided it.

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