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KATRIN_1 [288]
3 years ago
13

Prove the identity cos(x-y)-cos(x+y)=2sinxsiny

Mathematics
1 answer:
tekilochka [14]3 years ago
7 0

Answer:

see the procedure

Step-by-step explanation:

we know that

cos(X - Y) = cosX cosY + sinX sinY\\cos(X + Y) = cosX cosY - sinX sinY

so

cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-(cosX cosY - sinX sinY)

cos(X - Y)-cos(X + Y)=cosX cosY + sinX sinY-cosX cosY + sinX sinY

cos(X - Y)-cos(X + Y)=sinX sinY+ sinX sinY

cos(X - Y)-cos(X + Y)=2sinX sinY ----> is verified

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Answer:

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Here, we have a word problem.

The shows and frequency of watching are;

           

Show A                                   Every 2 days

Show B                                   Every 3rd day

Show C                                   Every 5th day

Show D                                   Every 10th day

Danny watched all four shows on August 1, therefore, the day he will watch all  four shows can be found by finding the Lowest Common Multiple, LCM of the frequency of his watching each of the shows. That is, the LCM of 2, 3, 5 and 10

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