Final answer:
The expression 5cos²x-5 simplifies to -5sin²x using the Pythagorean trigonometric identity.
Step-by-step explanation:
The expression given is 5cos²x-5. We can simplify this using the Pythagorean trigonometric identity, which states that sin²x + cos²x = 1. Therefore, we can express cos²x as 1 - sin²x. Substituting this into the original expression:
5cos²x - 5 = 5(1 - sin²x) - 5
a. Simplify by distributing the 5:
5 - 5sin²x - 5
b. Combining like terms:
-5sin²x
Thus, the original expression simplifies to the single trigonometric function -5sin²x, which has no denominator.