How do you solve cot^2x/(1+cscx)=cotx(secx-tanx)?

1 Answer
Jul 24, 2016

The question should say to prove, not to solve, because this equation is true to all values of x, making it an identity.

Explanation:

(csc^2x - 1)/(1 + cscx)=cosx/sinx(1/cosx - sinx/cosx)

((cscx + 1)(cscx - 1))/(cscx + 1)=1/sinx - 1

((cancel(cscx + 1))(cscx- 1))/cancel(cscx + 1) = 1/sinx - 1

cscx - 1=(1 - sinx)/sinx

1/sinx - 1=(1 - sinx)/sinx

(1 - sinx)/sinx = (1 - sinx)/sinx

Identity proven!!

Hopefully this helps!