Question
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Prove the identities.







Ask by Mckenzie Crawford. in South Africa
Mar 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Identities 1, 2, 3, 4, 5, 6, and 8 are true. Identity 7 is false.

Solution

Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Choose the other side to work on:
  • step3: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Choose the other side to work on:
  • step3: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Choose the other side to work on:
  • step3: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Verify the identity:

    Determine whether the expression is always true.
    Verify the identity by following steps:
  • step0: Verify:
  • step1: Choose a side to work on:
  • step2: Verify the identity:

    Here are the results for the identities you provided:
  1. Identity:
    Result: True
  2. Identity:
    Result: True
  3. Identity:
    Result: True
  4. Identity:
    Result: True
  5. Identity:
    Result: True
  6. Identity:
    Result: True
  7. Identity:
    Result: False
  8. Identity:
    Result: True

Summary:

  • Identities 1 to 6, and 8 are true.
  • Identity 7 is false.

Answered by UpStudy AI and reviewed by a Professional Tutor

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Explain
Simplify this solution

Extra Insights

To prove the first identity, we start with the left side:
.
Now, using the Pythagorean identity, , we find that , thus confirming the identity.
For the second identity, let’s simplify the left side:
.
Using the Pythagorean identity again, , we have , proving this identity as well!

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