Question
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 expressionis 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 expressionis always true.
Verify the identity by following steps: - step0: Verify:
- step1: Choose a side to work on:
- step2: Verify the identity:
Determine whether the expressionis 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 expressionis 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 expressionis always true.
Verify the identity by following steps: - step0: Verify:
- step1: Choose a side to work on:
- step2: Verify the identity:
Determine whether the expressionis always true.
Verify the identity by following steps: - step0: Verify:
- step1: Choose a side to work on:
- step2: Verify the identity:
Determine whether the expressionis 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:
-
Identity:
Result: True -
Identity:
Result: True -
Identity:
Result: True -
Identity:
Result: True -
Identity:
Result: True -
Identity:
Result: True -
Identity:
Result: False -
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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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.
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,