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rodikova [14]
3 years ago
14

HELP PLEASE 30 POINTS! WILL MARK BRAINLIEST IF CORRECT!!!!!

Mathematics
2 answers:
Flura [38]3 years ago
6 0

Answer:

this is a required answer.

KATRIN_1 [288]3 years ago
5 0

Answer:

See Below.

Step-by-step explanation:

We want to verify:

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

We will utilize the following identities:

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

And:

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

So, by substitution, we acquire:

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

Distribute:

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

The first and third term will cancel:

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

Combine like terms:

2\sin(x)\sin(y)\stackrel{\checkmark}{=}2\sin(x)\sin(y)

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