math
posted by kayla on .
how do I simplify these?
1. (Cot/1tan) + (Tan/1Cot)  Tan  Cot
2. (1+cos) (csccot)

sloppy notation.
the cot of what, the sin of what?
sin, cos, tan, etc are mathematical operators
I will use x as the "angle"
(Cotx/1tanx) + (Tanx/1Cotx)  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(sinxcosx)  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)(cosxsinx) and try to finish it. 
for the second, I would use the same approach.
(1+cosx) (cscxcotx)
= (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 
(cos/sin/(1  sin/cos) + sin/cos/(1cos/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(cs))  s^2/(c(cs))
1/(cs) * (c^2/s s^2/c)
1/(cs) * ( (c^3s^3)/sc)
1/(cs) * ((cs)(c^2 + sc + s^2)/sc
(1+sc)/sc
now put that 1/sc back
(1+sc)/sc  1/sc
sc/sc
1 Caramba !!!! 
It is the sins, cos, etc of theta

OK, I was not about to type theta all the time either, and in fact even got tired of typing sin and cos.