pleas solve cosA-sinA+1/cosA+sinA-1=cosecA+cotA  every step every thing in detail

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You need to verify if the expression is an identity such that:

`(cosA-sinA+1)/(cosA+sinA-1) = cscA+cotA`

You should multiply by `(cosA+sinA-1)`   both sides such that:

`cosA-sinA+1 = (cscA+cotA)(cosA+sinA-1)`

You should remember that `csc A = 1/sin A`  and `cot A = cos A/sinA` .

`cosA-sinA+1 = ((1+cosA)/sinA)(cosA+sinA-1)`

You need to multiply by sinA doth sides such that:

`sinA(cosA-sinA+1) = (1+cosA)(cosA+sinA-1)`

You need to open the brackets both sides such that:

`sinA*cosA - sin^2A + sin A = cosA + sinA - 1 + cos^2A + sinA*cosA - cosA`

You need to reduce by sinA, cosA and sinA*cosA such that:

`- sin^2A = - 1 + cos^2A `

You need to bring `sin^2A`  to the right side such that:

`0 = -1 + cos^2A + sin^2A `

You need to rememeber the fundamental formula of trigonometry such that:

`cos^2A + sin^2A = 1`

`0 = -1 + 1 =gt 0 = 0`

Hence, using some of trigonometric identities yields that the expression `(cosA-sinA+1)/(cosA+sinA-1) = cscA+cotA ` is an identity.

Sources:

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