Post a New Question

Trigonometry - Identities and proof

posted by .

Show that cot((x+y)/2) = - (sin x - sin y)/(cos x - cos y) for all values of x and y for which both sides are defined.

I tried manipulating both sides in terms of trig identities but I don't really have a would be appreciated, thanks.

  • Trigonometry - Identities and proof -

    Using the sum-to-product formulas,

    sinx-siny = 2cos((x+y)/2)sin((x-y)/2)
    cosx-cosy = -2sin((x+y)/2)sin((x-y)/2)

    now just divide to get

    cos((x+y)/2) / sin((x+y)/2) = cot((x+y)/2)

  • Trigonometry - Identities and proof -

    Two of the standard conversion formulas are:

    sinA - sinB = 2sin((A-B)/2) cos( (A+B)/2)
    cosA - cosB = - 2sin( (A-B)/2) sin( (A+B)/2)

    near bottom of page under:
    Sum-to-Product Formulas

    = -(sinx - siny)/(cosx - cosy)
    = - 2sin((X-Y)/2) cos( (X+Y)/2)/- 2sin( (X-Y)/2) sin( (X+Y)/2)
    = cos((X+Y)/2) / sin(X+Y)/2)
    = cot((X+Y)/2)

    = LS

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
  2. algebra

    Can someone please help me do this problem?
  3. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
  4. Trigonometry

    Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; …
  5. Math (Trig)

    sorry, another I can't figure out Show that (1-cot^2x)/(tan^2x-1)=cot^2x I started by factoring both as difference of squares. Would I be better served by writing in terms of sine and cosine?
  6. Trigonometry

    Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees …
  7. Trigonometry - Proof

    Prove that cot x + tan x = csc x * sec x whenever both sides are defined. I tried rewriting all sides in terms of sin x but it got all complicated and I can't make head or tail of it. Could someone assist me?
  8. Math-Trigonometry

    Show that if x, y, and z are consecutive terms of an arithmetic sequence, and tan y is defined, then (sin x + sin y + sin z) / (cos x + cos y + cos z) = tan y. So I tried letting x = y-k (since x,y,z are consecutive terms of an arithmetic …
  9. Trigonometry - Identities

    If tan 2x = - 24/7, where 90 degrees < x < 180 degrees, then find the value of sin x+ cos x. I applied various identities and tried manipulating the problem to get sin x + cos x = sin(arctan(-24/7)/2) + cos(arctan(-24/7)/2) I …
  10. Precalculus

    Show that cot((x+y)/2)=-(sin(x)-sin(y))/(cos(x)-cos(y)) for all values of x and y for which both sides are defined.

More Similar Questions

Post a New Question