Question

Trigonometry: Verify the following:
cot X +1/cot x - 1 = 1+ tan X/1-tanx
I got as far as: ((cos x/sinx) +1)/((cos x/sin x)-1) but then got stuck. The answer key shows the next step is ((cos x +sin x)/sin x)/((cos x - sin x)/sin x) but I don't understand how we got there. Can someone explain?

Answer 1

\[\cot x +\frac{1}{\cot x}-1=1+\frac{\tan x}{1}-tanx\]

Answer 2

That's what you posted. What is the real problem?

Answer 3

How is the grouping done for that? Whats in the numerator/denominator?

Answer 4

numerator cot x + 1 and denominator cot x - 1

Answer 5

next step I turned both cot into cos over sin

Answer 6

the third step is the step I don't understand:
numerator (cos x + sin x)/sin x and denominator (cos x - sin x)/sin x

I don't understand where the ones went and where the sins in the numerator came from.