Lesson Example Discussion Quiz: Class Homework |
Step-1 |
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 |
Use cofunction identities to simplify the expression \$ "csc"^2"x" − "tan"^2 (pi/2 − x) \$. |
|
2 |
Step |
The given expression is |
\$ "csc"^2"x" − "tan"^2 (pi/2 − x) \$ |
3 |
Step |
The cofunction identity for tangent is: |
\$ "tan"^2 (pi/2 − x) = "cot"^2"x" \$ |
4 |
Step |
Rewrite the given expression using the cofunction identity: |
\$ "csc"^2"(x)" − "cot"^2"(x)" \$ |
5 |
Formula: |
There is a Pythagorean identity relating cosecant and cotangent: |
\$ "csc"^2"(x)" = 1 + "cot"^2"(x)" \$ |
6 |
Step |
Substitute the identity \$ "csc"^2"(x)" = 1+ "cot"^2"(x)" \$ into the simplified expression: |
\$ (1 + "cot"^2"(x)") − "cot"^2"(x)" \$ ⇒ \$ 1 + "cot"^2"(x)" − "cot"^2"(x)" \$ ⇒ 1 |
7 |
Step |
Thus, the simplified expression for \$ "csc"^2"x" − "tan"^2 (pi/2 − x) \$ is 1. |
|
8 |
Choice.A |
The simplified expression is 1, which matches option A |
1 |
9 |
Choice.B |
The expression is incorrect as it stands because it simplifies to 1, not 60 |
60 |
10 |
Choice.C |
Option C is wrong as the simplified form doesn’t yield 0 but rather 1 |
0 |
11 |
Choice.D |
This choice is incorrect because the simplified expression is not "None of the above"; it simplifies to 1 |
None of the above |
12 |
Answer |
Option |
A |
13 |
Sumup |
Can you summarize what you’ve understood in the above steps? |
|
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