Question

Which of the following are antiderivatives of sec²(x)?

A. tan(x) + C
B. cot(x) + C
C. csc(x) + C
D. -cos(x) + C

Answer 1

The antiderivative of sec²(x) is tan(x) + C.

Step-by-step explanation:

The antiderivative of sec²(x) is tan(x) + C.

To find the antiderivative, you can use the trigonometric identity:

sec²(x) = 1 + tan²(x)

So, the antiderivative of sec²(x) is the antiderivative of (1 + tan²(x)). The antiderivative of 1 is x, and the antiderivative of tan²(x) is tan(x). Therefore, the antiderivative of sec²(x) is tan(x) + C, where C is the constant of integration.