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Identities 1, 2, 3, 4, 5, 6, and 8 are true. Identity 7 is false.
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To prove the first identity, we start with the left side:
.
Now, using the Pythagorean identity, , we find that
, thus confirming the identity.
Now, using the Pythagorean identity,
For the second identity, let’s simplify the left side:
.
Using the Pythagorean identity again, , we have
, proving this identity as well!
Using the Pythagorean identity again,