Question

PLEASE HELP ASAP!!! URGENT

Verify the identity. Sinx/1-cosx = cscx+cotx

Please use the answers shown in the image !! Thank you !!

Answer 1

1)
`(\sin x)/(1-\cos x) = \csc x + \cot x`

2)
`(\sin x)/(1-\cos x) = (1)/(\sin x) + (\cos x)/(\sin x)`

3)
`(\sin x)/(1-\cos x) = (1+\cos x)/(\sin x)`

4)
`(\sin x)/(1-\cos x) = (\sin x \cdot (1+\cos x))/(\sin^(2)x)`

5)
`(\sin x)/(1-\cos x) = (\sin x\cdot (1+\cos x))/(1-\cos^(2)x)`

6)
`(\sin x)/(1-\cos x) = (\sin x\cdot (1+\cos x))/((1+\cos x)\cdot (1-\cos x))`

7)
`(\sin x)/(1-\cos x) = (\sin x)/(1-\cos x)`

Explanation:

Now we proceed to show all steps needed to demonstrate the trigonometric identity:

1)
`(\sin x)/(1-\cos x) = \csc x + \cot x` Given.

2)
`(\sin x)/(1-\cos x) = (1)/(\sin x) + (\cos x)/(\sin x)` Identities for cosecant and cotangent functions.

3)
`(\sin x)/(1-\cos x) = (1+\cos x)/(\sin x)`
`(a)/(b)+(c)/(b) = (a+c)/(b)`

4)
`(\sin x)/(1-\cos x) = (\sin x \cdot (1+\cos x))/(\sin^(2)x)` Existence of additive inverse/Modulative property.

5)
`(\sin x)/(1-\cos x) = (\sin x\cdot (1+\cos x))/(1-\cos^(2)x)` Fundamental trigonometric identity.

6)
`(\sin x)/(1-\cos x) = (\sin x\cdot (1+\cos x))/((1+\cos x)\cdot (1-\cos x))` Factorization.

7)
`(\sin x)/(1-\cos x) = (\sin x)/(1-\cos x)` Existence of additive inverse/Modulative property/Result.