Originally Posted by

**Peritus** to solve this equation we'll use the following identities:

1. 1+(tan(x))^2 = 1/(cosx)^2

2. 1+(cot(x))^2 = 1/(sinx)^2

after applying them to the given equation we get:

(tan(x))^2 + cos(x) - sin(x) - (cot(x))^2 = 0

<=> [(sin(x))^4 - (cos(x))^4]/[(sin(x)*cos(x))^2] + cos(x) - sin(x) = 0

<=> (sin(x)^2 + cos(x)^2)*(sin(x)^2 - cos(x)^2) + (cos(x)^3)*(sin(x)^2) - (sin(x)^3)*(cos(x)^2) = 0

this equation holds only in those places where sin(2x)^2 doesn't vanish -> x != (pi/2) * k

<=> (sin(x) + cos(x))*(sin(x) - cos(x)) + (cos(x)^2)*(sin(x)^2)*[cos(x) - sin(x)] = 0

<=> (sin(x) - cos(x))*[sin(x) + cos(x) - (cos(x)^2)*(sin(x)^2)] = 0

sin(x) = cos(x)

as you've already mentioned one solution to the equation is pi/4 + pi*k...