How do you simplify [cos(x+2pi)]/sinx?

1 Answer
Shwetank Mauria
Feb 22, 2016

cos(x+2pi)/sinx = cotx

Explanation:

To simplify cos(x+2pi)/sinx, first one may note that adding 2pi or its multiple, to a trigonometric ratio, does not change its value

i.e. sin(x+2npi)=sinx (for all n, where n is an integer), cos(x+2npi)=cosx, tan(x+2npi)=tanx, cot(x+2npi)=cotx, sec(x+2npi)=secx and csc(x+2npi)=cscx.

Hence, cos(x+2pi)/sinx = cosx/sinx or cotx.

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