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"

=cosx/(1-sinx) multiply top and bottom by 1+sinx, (creating the difference of square pattern)
=cosx(1+sinx)/cos^2x divide by cosx
= (1+sinx)/cosx
= R.S.

Wow !!

  1. 👍 0
  2. 👎 0
  3. 👁 304
asked by abdo

Respond to this Question

First Name

Your Response

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 -

    asked by Dave on January 2, 2007
  2. Pre-calc

    prove the identity: (cosx)(tanx + sinx cotx)=sinx+cos(squared)x i need steps to show how i got the answer generally, it is a good idea to change all trig ratios to sines and cosines, and start with the more complicated-looking

    asked by Stacey on May 6, 2007
  3. Simplifying with Trigonometry Identities

    Hi, I am a senior in High School having a really difficult time with two problems. I have to prove using the trigonometric identities that they equal each other but I am having a really hard time trying to get them to equal each

    asked by amanda on March 7, 2007
  4. 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!

    asked by Jonathan on December 14, 2009
  5. Precalculus/Trig

    I can't seem to prove these trig identities and would really appreciate help: 1. cosx + 1/sin^3x = cscx/1 - cosx I changed the 1: cosx/sin^3x + sin^3x/sin^3x = cscx/1-cosx Simplified: cosx + sin^3x/sin^3x = cscx/1-cosx I don't

    asked by Heather on August 15, 2014
  6. 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] =

    asked by Anonymous on February 20, 2012
  7. Precalculus/Trig

    Prove the following identity: 1/tanx + tanx = 1/sinxcosx I can't seem to prove it. This is my work, I must've made a mistake somewhere: Converted 1/tanx: 1/sinx/cosx + sinx/cosx = 1/sinxcosx Simplified 1/sinx/cosx: cosx/sinx +

    asked by Heather on August 14, 2014
  8. 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

    asked by mo on April 18, 2007
  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)

    asked by Jessy on November 24, 2013
  10. trigonometry

    can i use factoring to simplify this trig identity? the problem is sinx + cotx * cosx i know the answer is cscx and i know how to get it but i want to know if i can do factoring to get it bc i tried to but it wont give me the

    asked by v on December 3, 2012

More Similar Questions