# what are the restrictions for the equation sin(angle)+cos(angle)cot(angle)=csc(angle)

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that cotangen and cosecant functions are rational function, `cot alpha = cos alpha/ sin alpha` , `csc alpha = 1/sin alpha` hence, the restrictions may be found solving the equation `sin alpha != 0` such that:

`sin alpha!= 0 =gt alpha != (-1)^n*sin^(-1)(0) + n*pi`

`alpha != n*pi`

Substituting `cos alpha/ sin alpha`  for `cot alpha ` and `1/sin alpha`  for `csc alpha`  yields:

`sin alpha + cos alpha*cos alpha/sin alpha = 1/sin alpha`

You need to bring the terms to the left to a common denominator such that:

`(sin^2 alpha + cos^2 alpha)/sin alpha = 1/sin alpha`

You need to remember the basic formula of trigonometry such that:

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

`1/ sin alpha = 1/sin alpha`

Hence, the last line proves that the expression `sin alpha + cos alpha*cot alpha = csc alpha`  is identity for all angles `alpha` , except the angles `alpha = n*pi` .