Question

Verify:

(cot x)/(1 + csc x) = (csc x - 1)/(cot x)

I realized that if I cross-multiplied:

(cot^2 x) = (csc^2 x - 1)
(cot^2 x + 1) = csc^2 x

Am I able to do this? Or is this technically incorrect?

Answer 1

you will be able to do

Answer 2

multiply the numerator and denominator by cosec x -1 and then simplify

Answer 3

cot x/ (cosex +1) = cotx *( (cosex -1) / ( (cosex -1)* (cosex +1))

Answer 4

= cotx *(cosecx -1) /(cosec^x-1 )
=cotx *(cosecx -1) / (cotx)^2
=(csc x - 1)/(cot x)

Answer 5

Okay. Thank you!

Answer 6

yw