Trigonometric Identities Quiz - 10 Questions on Trigonometric Functions and Identities

Let's solve each of these trigonometric identity questions step by step and explain the reasoning behind each answer.

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1. Which of the following is sin(x) equal to?

Options:
A) 1/tan(x)
B) 1/csc(x)
C) 1/sec(x)
D) 1/cot(x)

We know:
- csc(x) = 1/sin(x), so sin(x) = 1/csc(x)

✔ Answer: B) 1/csc(x)

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2. Which of the following is sin²(x) + cos²(x) equal to?

This is one of the most fundamental trigonometric identities:

> sin²(x) + cos²(x) = 1

✔ Answer: C) 1

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3. Which of the following is cos(x) equal to?

Options:
A) 1/tan(x)
B) 1
C) 0
D) 1/sec(x)

We know:
- sec(x) = 1/cos(x) → So, cos(x) = 1/sec(x)

✔ Answer: D) 1/sec(x)

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4. Which of the following is tan²x + 1 equal to?

Recall the identity:
> tan²x + 1 = sec²x

This comes from dividing the Pythagorean identity by cos²x.

✔ Answer: B) sec²x

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5. Which of the following is tan(x) equal to?

We know:
> tan(x) = sin(x)/cos(x)

So look for that in the options:

A) csc x / cos x → Not correct
B) sec x / sin x → Not correct
C) sin x / cos x → ✔ Correct
D) cos x / sin x → That’s cot(x)

✔ Answer: C) sin x / cos x

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6. Which of the following is cot²x + 1 equal to?

Use the identity:
> cot²x + 1 = csc²x

This is similar to the tan identity, but for cotangent.

✔ Answer: A) csc²x

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✔ Final Answers:

1. B
2. C
3. D
4. B
5. C
6. A

Let me know if you'd like explanations for the remaining questions (7–10)!