Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sabika13

  • 2 years ago

How do I solve this trig identity: cos2x/(1+sinx^2)=tan(pie/4 -x)

  • This Question is Closed
  1. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i think ur question is cos2x/(1+sin2x) now cos2x =cos^2x -sin^2x=(cosx+sinx)(cosx-sinx) and 1+sin2x = cos^2x + sin^2x +2sinxcosx =(cosx+sinx)^2 thus cos2x/(1+sinx)^2= (cosx+sinx)(cosx-sinx)/(cosx+sinx)^2 =(cosx- sinx)/((cosx+sinx) divide both num and denom by cosx and then we have =(1-sinx/cosx)/(1+sinx/cosx) =(1-tanx)/(1+tanx) = (tan(pi/4) -tanx)/(1+tan(pi/4)tanx)=tan(pie/4 -x)

  2. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    for the second last step.. where did the square roots go? isnt it suppose to be: (1-sinx/cosx)(1-sinx/cos)/(1+sinx/cos)(1+sinx/cosx)

  3. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    actually the factors (cosx+sinx) are there both in num and denom hence they cancel each other

  4. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but its (cosx-sinx) in the num :s

  5. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (cosx+sinx)(cosx-sinx) / (cosx+sinx)^2 =(cosx-sinx) / (cosx+sinx)

  6. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i hope its clear now

  7. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    why 13 u hv included in ur id ? if u don't mind

  8. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    if its (cosx+sinx)^2, it has to equal (cosx+sinx)(cosx+sinx)

  9. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idk random.

  10. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (cosx+sinx)^2= (cosx+sinx)(cosx+sinx) (correct ) that is why one of the (cosx+sinx)

  11. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    cancel each other

  12. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    how does cos^2x -sin^2x=(cosx+sinx)(cosx-sinx)

  13. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    USE ..A*A -B*B =(A)^2 -(B)^2 = (A+B)(A-B)...

  14. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay, then why isnt :(cosx+sinx)^2 --> (cosx-sinx)(cosx+sinx)

  15. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    bcoz a^2 =a*a

  16. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so (a+b)^2 =(a+b)(a+b)

  17. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but if u multiply (a+b)(a-b) u get (a^2 -b^2)

  18. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so (a^2-b^2) does not equal (a-b)^2 ?

  19. matricked
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    sahi hai..

  20. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh i get it..

  21. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    =(1-tanx)/(1+tanx) = (tan(pi/4) -tanx)/(1+tan(pi/4)tanx)=tan(pie/4 -x) can u explain that? .. where did pi/4 come from ?

  22. Dido525
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Tan (pi/4) = 1.

  23. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is that a trig identity?

  24. Dido525
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No. If you do that on a calculator you get that.

  25. Dido525
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Tan(pi/4) is always 1. Look on a unit circle.

  26. sabika13
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay, thanks!!

  27. Dido525
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Welcome :) .

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.