Does cotangent plus one equal cosecant?

Answer 1

Cotangent = 1/Tangent : Cosecant = 1/Sine

Then, cot + 1 = (1/tan) + 1 = (cos/sin) + (sin/sin) = (cos + sin)/ sin.

Now, cos² + sin² = 1 so for the statement to be valid the final expression would have to be : (cos² + sin² ) / sin = 1/sin.

As this is not the case then, cot + 1 ≠ cosec.

In fact, the relationship link is cot² + 1 = cosec²