A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Help with identities: 1. ( sin2x/sin x)-(cos2x/cos x)=sec 2. (cos x+cos y)^2 +(sin x-sin y)^2 =2+2cos(x+y)

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For question 1. it says the steps should be: apply the double-angle formulas for sine and cosine, then simplify the expression. I got this far. \[(2\sin x \cos x)/\sin x)-(2 \cos^2x-1)/\cos x)\] \[2 \cos x=(2 \cos^2 x-1)/\cos x\]

  2. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i don't think i am reading question 1. properly, can you type out the equation again (or draw it) please?

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

    \[\frac{ \sin (2x) }{ sinx }-\frac{ \cos(2x) }{ \cos x }=\sec x\]

  4. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ah, i can read it properly now, thakyou

  5. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    your working so far it good

  6. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you have \[LHS = 2 \cos x-\frac{2 \cos^2 x-1}{\cos x}\]

  7. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now break up the fraction like this \[\frac{a+b}{c}=\frac ac+\frac bc\]

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ 2\cos^2 }{ \cos }=2 \cos\] \[\frac{ -1 }{ \cos}=-\sec\] Is this right?

  9. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right!, (becareful with the extra -sign, outside of the big fraction)

  10. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so you've got \[LHS = 2\cos x-\frac{2 \cos^2 x-1}{\cos x}\\ \qquad=2\cos x-\left(\frac{2 \cos^2 x}{\cos x}+\frac{-1}{\cos x}\right)\\ \qquad=2\cos x-\left(2\cos x-\sec x\right)\\\qquad=\]

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2 cos x-2cos x=0 -sec x=sec x ?

  12. UnkleRhaukus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    be CAREFUL with the minus signs. \[\qquad=2\cos x-\left(2\cos x-\sec x\right)\\\qquad=2\cos x-2\cos x+\sec x\\\qquad=\]

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Ahhhh okay, I got it now!

  14. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.