Lesson Example Discussion Quiz: Class Homework |
Step-4 |
Title: Trigonometry Identities (quotient , co-function) |
Grade: 1300-a Lesson: S3-L4 |
Explanation: Hello Students, time to practice and review the steps for the problem. |
Lesson Steps
| Step | Type | Explanation | Answer |
|---|---|---|---|
1 |
Problem |
Find the value of \$\sqrt (("cscA" times "cscB" ) times 1/(("sinA"/"sinB") + ("cosA"/"cosB"))) \$ such that A and B are two complementary angles. |
|
2 |
Step |
The given expression is |
\$\sqrt (("cscA" times "cscB" ) times 1/(("sinA"/"sinB") + ("cosA"/"cosB"))) \$ |
3 |
Hint |
The given A and B two complementary angles so A = 90° - B and B = 90° - A |
|
4 |
Step |
Now plug the hint in the given expression |
⇒ \$\sqrt(("cscA" "csc"(90 - "A")) times 1/{("sinA"/("sin"(90 - "A"))) + ("cosA" / ("cos"(90 - "A")))})\$ ⇒ \$\sqrt("cscA" "secA" times 1)/{("sinA"/"cosA") + ("cosA" / "sinA")}\$ |
5 |
Step |
After simplification |
⇒ \$\sqrt(("cscA" "secA" times 1/ {("sin"^2("A") + "cos"^2("A")) /("sinA""cosA")})\$ \$"sin"^2"A" + "cos"^2"A" =1\$ ⇒ \$\sqrt ("cscA" "secA" times "sinA" "cosA")\$ ⇒ 1 |
6 |
Step |
Therefore the simplified expression is 1. |
|
7 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
|
8 |
Choice.A |
This is not correct because it doesn’t provide a definitive value for the expression |
2 |
9 |
Choice.B |
This is incorrect because the expression does have a 0, which is 1 |
0 |
10 |
Choice.C |
This is correct because the expression simplifies to 1 for any complementary angles A and B |
1 |
11 |
Choice.D |
This is incorrect because the expression does have a value, which is 1 |
None of these above |
12 |
Answer |
Option |
C |
13 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
|
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