Question

What are the solutions to the equation tan(x)sin(x) - tan(x) = 0 in the interval 0, 2π?

A. x = 0, π, 2π
B. x = π/2, 3π/2, 5π/2
C. x = 0, π/2, π
D. x = π/4, 5π/4, 3π/4

Answer 1

The solutions to the equation tan(x)sin(x) - tan(x) = 0 in the interval 0, 2π are x = 0, π, 2π, π/2, 3π/2.

Step-by-step explanation:

The equation is tan(x)sin(x) - tan(x) = 0. To solve this equation, we can factor out the common factor of tan(x). So the equation becomes tan(x)(sin(x) - 1) = 0. To find the solutions, we set each factor equal to zero:

• tan(x) = 0: This equation is satisfied when x = 0, π, 2π.
• sin(x) - 1 = 0: This equation is satisfied when x = π/2, 3π/2.

Therefore, the solutions to the equation in the interval 0, 2π are x = 0, π, 2π, π/2, 3π/2, which corresponds to option A.