Values and IdentitiesProve the identitiessinh (x + y) =

Chapter 7, Problem 11E

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QUESTION:

Problem 11E

Values and Identities

Prove the identities

sinh (x + y) = sinh x cosh y + cosh x sinh y,

cosh (x + y) = cosh x cosh y + sinh x sinh y.

Then use them to show that

a. sinh 2x = 2 sinh x cosh x.

b. cosh 2x = cosh2 x + sinh2 x.

Questions & Answers

QUESTION:

Problem 11E

Values and Identities

Prove the identities

sinh (x + y) = sinh x cosh y + cosh x sinh y,

cosh (x + y) = cosh x cosh y + sinh x sinh y.

Then use them to show that

a. sinh 2x = 2 sinh x cosh x.

b. cosh 2x = cosh2 x + sinh2 x.

ANSWER:

Solution:

Step 1 of 4:

In this problem, we need to prove the given identities.

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