solve the identity csc x - cot x = sin x / 1+cos xStep by step instructions please.
You need to remember that `csc x = 1/ sin x` and `cot x = cos x/sin x` , hence, substituting `1/sin x` for `cscx` and `cos x/sin x` for `cot x,` to the left side, yields:
`1/ sin x - cos x/sin x = (sin x)/(1 + cos x)`
`(1 - cos x)/sin x= (sin x)/(1 + cos x)`
Performing diagonal multiplication yields:
`sin^2 x = (1 - cos x)(1 + cos x)`
Converting the product into a difference of squares yields:
`sin^2 x = 1 - cos^2 x`
Moving the term `cos^2 x` to the left side yields:
`sin^2 x + cos^2 x = 1`
Notice that solving the expression you have arrived to the fundamental formula of trigonometry, hence, the given expression represents the equivalent of fundamental formula `sin^2 x + cos^2 x = 1` , hence `csc x - cot x = (sin x)/(1 + cos x)` holds.