Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathslover Group Title

If \(\cos(x-y)\) , \(\cos x \) and \(\cos (x+y)\) are in Harmonic progression. then evaluate \(|\cos x . \sec (\frac{y}{2})|\)

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    i tried to do like this first.

    • one year ago
    1 Attachment
  2. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Should I simplify it further?

    • one year ago
  3. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Or I am going on wrong track?

    • one year ago
  4. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I have : \(\cfrac{2\cos (x+y) \cos (x-y) }{\cos (x-y) + \cos (x+y)}= \cos x\) Now : \(2\cos (x+y ) \cos (x-y) = \cos x \cos (x-y) + \cos x \cos (x+y)\) \(\implies 2\cos^2x \cos^2y - 2\sin^2 x \sin^2 y = \cos x ( \cos (x+y) + \cos (x-y))\) \(\cfrac{2(\cos^2x \cos^2y - \sin^2x \sin^2y) }{\cos(x+y) + \cos(x-y)}= \cos x\) \(\cfrac{\cos^2x \cos^2y - \sin^2x \sin^2y}{\cos x\cos y }= \cos x\) \(\cos^2x\cos^2y - \sin^2x \sin^2y = \cos^2x \cos y\) \(\cos^2x \cos^2y - \cos^2 x \cos y = \sin^2x \sin^2y\) \(\cos^2x \cos^2y - \cos^2 x \cos y = (1-\cos^2x)(1-\cos^2y)\) \(\cos^2x\cos^2y-\cos^2x\cos y = 1 - \cos^2y - \cos^2x + \cos^2x\cos^2y\) \(\cancel{cos^2x\cos^2y} - \cos^2x \cos y = 1 - \cos^2y - \cos^2x + \cancel{\cos^2x\cos^2y}\) \(-\cos^2x\cos y = 1-\cos^2y - \cos^2x\) \(1-\cos^2y - \cos^2x + \cos^2x \cos y = 0 \) \((1+\cos y)(1+\cos y) - \cos^2x (1 - \cos y) = 0\) \((1-\cos y)(1+\cos y - \cos^2x ) = 0\) Therefore cos y = 1 and \(\cos x = \sqrt{2}\)

    • one year ago
  5. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    So I get : | \(\sqrt{2}\) | = \(\sqrt{2}\) @amistre64 would you please take time to check my method.

    • one year ago
  6. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Any help @UnkleRhaukus ?

    • one year ago
  7. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73 No clue?

    • one year ago
  8. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    it looks like you have done a ton of work, but i cannot do this in a few minutes, would take me at least an hour i can look at it later, it is real math not off the top of my head math

    • one year ago
  9. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    No problem but it didn't take me more than 10 minutes. Trust me ... its not that leanthy.

    • one year ago
  10. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    all though a quick google search tells me your answer is right

    • one year ago
  11. satellite73 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    and gives a slightly shorter method here is the link but ignore it if you want http://www.qfak.com/education_reference/science_mathematics/?id=b717416#.UUsQ1BesiSo

    • one year ago
  12. mathslover Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    great! Thanks.. A medal deserves

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.