Ask questions and get helpful responses.

math

3 cos^2 𝛼 + 2 cos^2 𝛽 =4
3 sin 2 𝛼 βˆ’ 2sin 2 𝛽=0
Find the values of cos 2𝛼 and cos 2𝛽.

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. I already did this for you. Take the trouble to read it this time, ok?
    since sin^2 + cos^2 = 1, the 2nd equation becomes
    3(1-cos^2 𝛼) βˆ’ 2(1-cos^2 𝛽) = 0
    3 - 3cos^2 𝛼 βˆ’ 2 + 2cos^2 𝛽 = 0
    Now the two equations read
    3cos^2 𝛼 + 2cos^2 𝛽 = 4
    -3cos^2 𝛼 + 2cos^2 𝛽 = -1
    subtract to get
    6cos^2𝛼 = 5
    cos^2𝛼 = 5/6
    Now just finish solving for cos^2𝛼 and cos^2𝛽
    Then use your double-angle formula
    cos 2x = 2cos^2x - 1

    post your work if you get stuck, but don't just post the same problem all over again.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Still need help? You can ask a new question.