trigonometry

if sin2x=3sin2y,
prove that:
2tan(x-y)=tan(x+y)

( here, in sin2x, 2x is an angle., like there's a formula:sin2x=2sinxcosx and sin2y=2sinycosy; ....)

  1. 👍 0
  2. 👎 1
  3. 👁 1,134
  1. It cannot be proven because it is not true. You can prove that by choosing x and y that satisfies sin2x=3sin2y. For example, take x = 15 degrees and y = 9.5941 degrees.
    For those choices, sin 2x = 3sin 2y = 0.500
    For those choices of x and y
    2 tan(x-y) = 0.1893 and tan (x+y) = 0.4577

    By being able to find ANY x,y combination that satisfies sin2x=3sin2y, and for which your second equation is not true, then your contention is disproved.

    Either someone is playing a practical joke on us, or on you, or you have copied the problem incorrectly

    1. 👍 0
    2. 👎 6
  2. I made a mistake in my example. Choose the angles x = 15 degrees and y = 4.79703 degrees. Then the condition
    sin 2x = 3 sin 2y is satisfied.
    2tan(x-y) = 0.35996
    tan (x+y) = 0.35996

    Your identity is almost certainly correct and I must apologize for my error in the previous answer.

    I tried to prove the second equation for any x and y that satisfy your first equation, but was not able to.

    1. 👍 0
    2. 👎 0
  3. give the proper solution for it. not by substituting values of x and y

    1. 👍 0
    2. 👎 0
  4. sin2x=3sin2y then prove 2tan(x-y)=tan(x+y)

    1. 👍 0
    2. 👎 2
  5. if sin2x=3sin2y
    then sin2x/sin2y=3/1
    sin2x+sin2y/sin2x-sin2y=3+1/3-1 (using conponendo and dividend rule)
    now using formula of sin2x+sin2y and sin2x-sin2y
    2sin (x+y)×cos (x-y)/2cos (x+y)×sin (x-y)=4/2
    solving this we get the result

    1. 👍 4
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. advanced function

    pls. help: prove the identity sin2x+sin2y=2sin(x+y)cos(x-y)

  2. Trig

    Find all the solutions in the interval [0,2pi). 2sin2x - sqrt(2) = 0 sin2x = sqrt(2)/2 I'm confused by the double angle. Please help.

  3. dai so

    chung minh dang thuc (1+Sin2x)/Cos2x=Tan(pi/4+x)

  4. Trigonometry

    Prove: 1-tanx/1+tanx=1-sin2x/cos2x

  1. Inverse trigonometry

    Prove that- tan^-1(1/2tan 2A)+tan^-1(cotA)+tan^-1(cot^3A) ={0,ifpi/4

  2. Math

    Prove the identity: sec^4x - tan^4x = 1+2tan^2x

  3. Pre-calculus

    prove the identity sin2x-sin2y/sin2x+sin2y=tan(x-y)/tan(x+y)

  4. trig

    Which expression is equivalent to tan(-x)cos^2x? -sin xcos x sin xcos x tan x + sin2x tan x − sin2x -tan x − sin2x

  1. trig

    sinx = 4/5 and x terminates in Quadrant II Find sin2x and cos2x How to get the answers, which are sin2x = -24/25, cos2x = -7/25?

  2. trig

    prove that the equation 2sin x cos x +4cos^2 x =1 may be written in the form of tan^2 x -2tan x -3=0

  3. trig

    sin2x=cos3x then sinx=?(if 0

  4. Maths

    Prove that sin2x+cos2x-1/sin2x+cos2x+1=tanx

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