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When simplifying using trigonometric identities, what is the result of sin²x - cos²x?

a) -1
b) 1
c) 2sinx
d) 2cosx

User Robbietjuh
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1 Answer

4 votes

Final answer:

The simplification of sin²x - cos²x using common trigonometric identities results in either 1 - 2cos²x or 2sin²x - 1. None of the given answer choices match these expressions. Further context is needed to provide a definitive answer.

Step-by-step explanation:

When simplifying using trigonometric identities, the result of sin²x - cos²x is found using the Pythagorean identity which states that sin²x + cos²x = 1. If we rearrange this identity, we can express sin²x as (1 - cos²x) and cos²x as (1 - sin²x).

Using these expressions, sin²x - cos²x can be rewritten as (1 - cos²x) - cos²x = 1 - 2cos²x. Similarly, using the other expression it can be rewritten as sin²x - (1 - sin²x) = 2sin²x - 1. However, neither of these forms simplifies directly to any of the given options (a) -1, (b) 1, (c) 2sinx, or (d) 2cosx.

To simplify further, one must know additional context or conditions. Without such context, the most we can infer is that sin²x - cos²x transforms into 1 - 2cos²x or 2sin²x - 1. None of the answer choices directly match these expressions. Therefore, a definitive choice from the given options cannot be made without further information.

User Dave Mateer
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