Question

Verify each identity:

Answer 1

\[\frac{ \sin \theta }{ 1-\cot \theta }-\frac{ \cos \theta }{ \tan \theta -1 }= \sin \theta + \cos \theta\]

Answer 2

i would start by changing the cot. in terms of tangent
getting the denominator with tan instead of cot

Answer 3

nevermind. after some work that doesn't do any good.

Answer 4

get common denominator first. then all algebra operations. its tedius.

Answer 5

how would i do that? :)

Answer 6

(sin(tan-1)/(1-cot)(tan-1))-(cos(1-cot)/(1-cot)(tan-1))= sin+cos

Answer 7

do it like an algebra problem. forget about the trig functions as something mysterious. they're just expressions

Answer 8

this problem is so long. type out your work step by step and ill tell you if your doing it right. so much to type out

Answer 9

did you get it? i can maybe attach a pic of my work. but its a lot to look at

Answer 10

I got it :) thanks!

Answer 11

looking at it again. i am curious if there is a way to do it working only from the LHS i spent about 3 hours messing with it and couldnt get it equal. have you tried?

Answer 12

@hartnn maybe you know if there is a way??

Answer 13

yeah

first convert everything into sin and cos

write cot as cos/sin
write tan as sin/cos

what u get ?

Answer 14

sin(1-cos/sin)-cos(sin/cos-1)=sin+cos
sin-cos-sin+cos=sin+cos
sin-sin+cos-cos=sin+cos
0=sin+cos?
i must have made a mistake im not seeing it though.

Answer 15

wait i think i see it. give me a sec

Answer 16

but its sin / (1-cot)
you seemed to have simplified
sin (1-cot)

Answer 17

im am to 1/sin-cos and i dont remember what is legal at this point.

Answer 18

ya i realized that. i would have to do the reciprocal

Answer 19

this time i did
sin(1/(sin/sin-cos/sin)-cos(1/(sin/cos-cos/cos)=sin+cos
then i got
sin/(sin-cos/sin)-cos/(sin-cos/cos)
then to
sin^2/(sin-cos)-cos^2/(sin-cos)
then
sin^2-cos^2/(sin-cos). can i factor a sin-cos out of the top and cancel them to get sin+cos?

Answer 20

absolutely correct!

Answer 21

whew! i spent a lot of time making mistakes. good practice though. its bad when your dreaming about trig identities ha

Answer 22

lol, but good work though :-)

Answer 23

thanks for the help. your a heck of a guy. i don't care what Vegeta says about you.

Answer 24

haha, i don't care either :P