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 and try to change it to the "easier" side.

so here goes....

LS=
sinx/cosx ÷ (1-cosx/sinx) + cosx/sinx ÷(1-sinx/cosx)
=sinx/cosx [sinx/(sinx-cosx) + cosx/sinx [cosx/(cosx-sinx)
=sin^2 x/(cosx(sinx-cosx)) - cos^2 x/(sinx(sinx-cosx))
= (sin^3x - cos^3 x)/(sinxcosx(sinx-cosx))
=(sinx-cosx)(sin^2x + sinxcosx + cos^2)÷[sinxcosx(sinx-cosx)] difference of cubes!!!
= (sin^2x + cos^2x + sinxcosx)/(sinxcosx)
= (1 + sinxcosx)/sinxcosx

R.S.= 1+ 1/(sinxcosx)
=(sinxcosx + 1)/(sinxcosx) = L.S

Wow!!
=

thank you very much for your help .

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. advanced functions

    Prove that cscx / cosx = tanx + cotx

  2. arithmetic

    if tanx+cotx=2 then the value of tan^5x + cot^10x is

  3. Pre-calculus

    Prove the following identities. 1. 1+cosx/1-cosx = secx + 1/secx -1 2. (tanx + cotx)^2=sec^2x csc^2x 3. cos(x+y) cos(x-y)= cos^2x - sin^2y

  4. Math please help quick

    Which of the following are identities? Check all that apply. (Points : 2) sin2x = 1 - cos2x sin2x - cos2x = 1 tan2x = 1 + sec2x cot2x = csc2x - 1 Question 4. 4. Which of the following equations are identities? Check all that

  1. trignometry

    tanx+cotx=5 than find the value of tan^2x+cot^2x

  2. college trigonometry

    verify identity: (tanx-cotx)/sinxcosx=sec^2x csc^2x

  3. Math

    1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d=sinw(t) for the simple harmonic motion. 2) Verify the identity tan^2X-cot^2X/tanX+cotX=tanX-cotX I'm not

  4. math

    sin2x-cotx = -cotxcos2x Using the various trigonometric identities(i.e. double angle formulas, power reducing formulas, half angle formulas, quotient identities, etc.) verify the identity. I first added cotx to both sides to get

  1. math

    Prove the identity: 1-cos2x/sin2x = 1+tanx/1+cotx I simplified the RS to tanx. LS:(1-2cos²x+1)/2sinxcosx (2+2cos²x)/2sinxcosx How do I simplify the rest?

  2. Trigonometry

    Prove that tanx+cotx=2sec(2x) Thank you! :)

  3. math

    If e^y=tanx, 0

  4. trigonometry

    Prove cotx-1/cotx+1=1-sin2x/cos2x

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