Question

Which of the following are identities?

check all that apply
A. cot²ˣ + 1 = csc²ˣ
B. tan² = 1 - sec²ˣ
C. sin 2ˣ - 1 = cos²ˣ
D. sin²ˣ + cos²ˣ = 1

Answer 1

Among the provided options, A (cot²x + 1 = csc²x) and D (sin²x + cos²x = 1) are correct trigonometric identities.

Step-by-step explanation:

The student is asking which of the options provided are identities in trigonometry. Let's examine each one:

• A. cot²x + 1 = csc²x is an identity known as the cotangent identity, which can be derived from the Pythagorean identity using the relationships between the trigonometric functions.
• B. tan²x = 1 - sec²x is not an identity. The correct form should be tan²x = sec²x - 1.
• C. sin 2x - 1 = cos²x is not an identity. The correct form would involve sin²x within the Pythagorean identity, not sin 2x.
• D. sin²x + cos²x = 1 is the fundamental Pythagorean identity in trigonometry and always holds true for any angle x.

Based on the analysis, the correct identities are option A and option D.