Question

how would i use the x,y, and r definitions of sinx and cosx to prove the identity (cosθ)/1-sinθ=(1+sinθ)/cosθ

Answer 1

sinx=y/r
cosx=x/r

Answer 2

this is what i did
\[(x/r)/(1-y/r)= (1+y/r)/(x/r)\]\[(x/r)-(y/r)=(x/r)+(y+r)\]\[(x-y)/r=(x+y)/r\]

... :S

Answer 3

cross multiply 1º line:
\[(x/r)^{2}=1-(y/r)^{2}----->\cos ^{2}x=1-\sin ^{2}x\]

Answer 4

so i have to do (x/r)^2/(1-y/r)^2 = (1+y/r)^2/(x/r)^2
and then work from there? :S ....

Answer 5

no

Answer 6

from what you did, take first line and cross multiply it

Answer 7

(x/r)(x/r)=(1+y/r)(1-y/r)

Answer 8

so i move the x/r to the left side and the 1-y/r to the right ?

Answer 9

yes

Answer 10

got it?

Answer 11

yep. since (x/r)^2 = 1-(y/r)^2
or cos^2x=1-sin^2x

Answer 12

thank you !

Answer 13

yw