How do you solve csc(x)+cot(x)=1 csc(x)+cot(x)=1?

1 Answer
Aug 12, 2018

x=npi+(-1)^n*(pi/2), n in ZZ.

Explanation:

Given that, cscx+cotx=1..............(star_1).

We know that, csc^2x-cot^2x=1.

"Factoring, "(cscx+cotx)(cscx-cotx)=1.

:. (1)(cscx-cotx)=1.........[because, (star_1).

:. cscx-cotx=1.............................(star_2).

(star_1)+(star_2) rArr 2cscx=2, or, cscx=1.

:. sinx=1=sin(pi/2).

Since, sintheta=sinalpha rArr theta=npi+(-1)^nalpha, n in ZZ,

:. sinx=sin(pi/2) rArr x=npi+(-1)^n*(pi/2), n in ZZ.