Math

if sinA+sinB=x and cosA-cosB=y then find tan[(A-B)/2]

  1. 👍
  2. 👎
  3. 👁
  1. use your sum-to-product formulas.
    sinA + sinB = 2 sin (A+B)/2 cos (A-B)/2
    now use the formula for sum of cosines, and recall that
    tanθ = sinθ / cosθ

    1. 👍
    2. 👎
    👤
    oobleck
  2. Two of the lesser known identities are:
    sinA + sinB = 2sin[(A+B)/2]cos[(A-B)/2] and
    cosA - cosB = -2sin[A+B)/2]sin[A-B)/2]
    so
    x/y = ( 2sin[(A+B)/2]cos[(A-B)/2] ) / (-2sin[A+B)/2]sin[A-B)/2] )
    x/y = - cos[(A-B)/2] / sin[A-B)/2]
    x/y = - cot[(A-B)/2]
    tan[(A-B)/2] = -y/x

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    If A and B are acute angle such that SinA=8/17 and CosB=3/5.Find 1, Cos(A+B) 2, Sin(A+B) 3, Sin(A-B)

  2. Pre-Calculus

    If sinA=3/5 when pi/2 < A < pi and cosB=5/13 when 3pi/2 < B < 2pi, find the exact value of the function cos(5pi/6+B).

  3. math

    prove that 1-tan 4 A by1+tan 4 A =cosA + sinA by cosA - sinA

  4. Maths, Divine International Public School

    If 15Cot=8, find (1+SinA)(1-SinA)/(1+CosA)(1-CosA)

  1. Trigonometry

    If sinA + sinB = a and cosA + cosB = b, find the value of tanA-B/2

  2. Math

    If 1/sinA+1/cosA =1/sinB+1/cosB, prove that: cot(A/2+B/2) = TanA. TanB

  3. Trigonometry

    Prove that 1-cosA+cosB-cos(A+B)/1+cosA-cosB-cos(A+B) = tanA/2cotA/2

  4. trigonometry

    Prove : 1 + Sin2A/ Cos2A = CosA + SinA / CosA- SinA

  1. math

    If A + B + c = 180 then show that sinA + sinB + sinC=4cosA/2. cosB/2 . cosC/2

  2. trig

    If A+B+C=^(^=180) prove that sinA + sinB - sinC = 4sinA/2 sinB/2 cosC/2

  3. Math

    prove that sinA/(1+cosA) + (1+cosA)/(sinA) = 2cosecA

  4. math

    12. IF 1/SinA+1/CosA=1/SinB+1/CosB ,PROVE THAT: Cot{(A+B)/2}=TanA.TanB

You can view more similar questions or ask a new question.