Ask Question

Find all solutions in the interval [0, 2π).

2 sin2x = sin x

Answers:

x = π/3, 2π/3

x = π/2, 3π/2, π/3, 2π/3

x = 0, π, π/6, 5π/6

x = π/6, 5π/6

+3
Answers (1)
  1. 2 May, 06:13
    0
    2sin^2 (x) = sinx

    we switch sinx from left to right and take sinx in front of brackets.

    sinx * (2sinx - 1) = 0

    now we need to solve 2 cases.

    first:

    sinx = 0

    that is for x = 0 and x = pi

    second:

    2sinx - 1 = 0

    2sinx = 1

    sinx = 1/2

    x = pi/6 or 5pi/6

    the case we had here is something like a*b=0 so either a=0 or b=0 thats why we solved problem this way.

    At the end comparing our results with options we can see that answer is third option.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Find all solutions in the interval [0, 2π). 2 sin2x = sin x Answers: x = π/3, 2π/3 x = π/2, 3π/2, π/3, 2π/3 x = 0, π, π/6, 5π/6 x = π/6, ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers