Advanced Functions

posted by .

Determine the solutions for:

(cos x)/(1 + sinx) + (1 + sinx)/(cosx) = 2

in the interval x is all real numbers, such that [-2 pi, 2pi]

  • Advanced Functions -

    Multiply each term by cosx(1+sinx)

    cos^2(x) + 1 + 2sinx + sin^2(x) = 2cosx(1+sinx)
    2 + 2sinx = 2cosx(1+sinx) , recall sin^2(x) + cos^2(x) = 1

    2(1 + sinx) = 2cosx(1+sinx)

    now divide by 1+sinx to get

    1 = cosx

    for the given domain, x = -2pi,0,2pi

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Pre-Calc

    Trigonometric Identities Prove: (tanx + secx -1)/(tanx - secx + 1)= tanx + secx My work so far: (sinx/cosx + 1/cosx + cosx/cosx)/(sinx/cos x - 1/cosx + cosx/cosx)= tanx + cosx (just working on the left side) ((sinx + 1 - cosx)/cosx)/((sinx …
  2. Trigonometry.

    ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! Generally these are done by changing everything to sines and cosines, unless you see some obvious identities. Also generally, it is best to start with the more complicated side …
  3. Trig........

    I need to prove that the following is true. Thanks (cosx / 1-sinx ) = ( 1+sinx / cosx ) I recall this question causing all kinds of problems when I was still teaching. it requires a little "trick" L.S. =cosx/(1-sinx) multiply top and …
  4. advanced functions

    Determine approximate solutions for this equation in the interval x is all real numbers [0, 2pi), to the nearest hundredth of a radian: cosx + 0.75 = 0
  5. Advanced Functions

    Determine all solutions in the interval x is all real numbers , [0, 2 pi] using a trigonometric identify 2cos^2x + sinx - 1 = 0
  6. Math - Pre- Clac

    Prove that each of these equations is an identity. A) (1 + sinx + cos x)/(1 + sinx + cosx)=(1 + cosx)/sinx B) (1 + sinx + cosx)/(1 - sinx + cosx)= (1 + sin x)/cosx Please and thankyou!
  7. maths - trigonometry

    I've asked about this same question before, and someone gave me the way to finish, which I understand to some extent. I need help figuring out what they did in the second step though. How they got to the third step from the second. …
  8. Trigonometry Check

    Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [cosx-(sin90cosx-cos90sinx)sinx]/[cosx-(cos180cosx+sinx180sinx)tanx] = [cosx-((1)cosx-(0)sinx)sinx]/[cosx-((-1)cosx+(0)sinx)tanx] = [cosx-cosxsinx]/[cosx+cosxtanx] = [cosx(1-sinx]/[cosx(1+tanx] …
  9. Trigonometry

    Prove the following trigonometric identities. please give a detailed answer because I don't understand this at all. a. sin(x)tan(x)=cos(x)/cot^2 (x) b. (1+tanx)^2=sec^2 (x)+2tan(x) c. 1/sin(x) + 1/cos(x) = (cosx+sinx)(secx)(cscx) d. …
  10. Calculus

    determine the absolute extreme values of the function f(x)=sinx-cosx+6 on the interval 0<=x<=2pi. This is what i did: 1.) i found the derivative of the function which is f'(x)=cosx+sinx 2.) I set f'(x)=0 and got sinx/cosx=-1 …

More Similar Questions