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May 22, 2015

Posted by **kayla** on Tuesday, February 10, 2009 at 6:19pm.

1. (Cot/1-tan) + (Tan/1-Cot) - Tan - Cot

2. (1+cos) (csc-cot)

- math -
**Reiny**, Tuesday, February 10, 2009 at 7:00pmsloppy notation.

the cot of what, the sin of what?

sin, cos, tan, etc are mathematical operators

I will use x as the "angle"

(Cotx/1-tanx) + (Tanx/1-Cotx) - Tanx - Cotx

I usually change everybody to sines and cosines, so ...

= (cosx/sinx)/(1 - sinx/cosx) + (sinx/cosx)/(1 - cosx/sinx) - sinx/cox - cosx/sinx

= (cos^2 x)/(sinx(cosx - sinx)) + (sin^2x)/(cosx(sinx-cosx) - sinx/cosx - cosx/sinx

= (cos^2 x)/(sinx(cosx - sinx)) - (sin^2x)/(cosx(cosx - sinx) - sinx/cosx - cosx/sinx

= .lots of messy typing here

form a common denominator of

(sinx)(cosx)(cosx-sinx) and try to finish it.

- math -
**Reiny**, Tuesday, February 10, 2009 at 7:09pmfor the second, I would use the same approach.

(1+cosx) (cscx-cotx)

= (1 + cosx)(1/sinx - cosx/sinx)

= 1/sinx - cosx/sinx + cosx/sinx - cos^2x/sinx

= 1/sinx(1 - cos^2x)

= 1/sinx(sin^2x_

= sinx

- math -
**Damon**, Tuesday, February 10, 2009 at 7:18pm(cos/sin/(1 - sin/cos) + sin/cos/(1-cos/sin) - sin/cos - cos /sin

multiply top and bottom of all by sin cos

cos^2/(sin cos -sin^2) + sin^2/(sin cos - cos^2) - (sin^2+cos^2)/sin cos

cos^2/(sin cos -sin^2) + sin^2/(sin cos - cos^2) - 1 /sin cos

cos^2/(sin (cos -sin)) - sin^2/(cos(cos - sin)) - 1 /sin cos

writing cos as c and sin as s

just doing first two terms for now

c^2/(s(c-s)) - s^2/(c(c-s))

1/(c-s) * (c^2/s -s^2/c)

1/(c-s) * ( (c^3-s^3)/sc)

1/(c-s) * ((c-s)(c^2 + sc + s^2)/sc

(1+sc)/sc

now put that -1/sc back

(1+sc)/sc - 1/sc

sc/sc

1 Caramba !!!!

- math -
**kayla**, Tuesday, February 10, 2009 at 7:22pmIt is the sins, cos, etc of theta

- math -
**Damon**, Tuesday, February 10, 2009 at 7:28pmOK, I was not about to type theta all the time either, and in fact even got tired of typing sin and cos.