What is the general solution for cot(x)(tan(x)-1)=0 ?

The general solution for cot(x)(tan(x)-1)=0 is x= pi/4+pin

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cot(x)(tan(x)-1)=0

cot (x) (tan (x) - 1) = 0

x = \frac{π}{4} + πn

Solution steps

cot (x) (tan (x) - 1) = 0

Solving each part separately

cot (x) = 0 or tan (x) - 1 = 0

cot (x) = 0 : x = \frac{π}{2} + πn

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{2} + πn, x = \frac{π}{4} + πn

Since the equation is undefined for:

\frac{π}{2} + πn

x = \frac{π}{4} + πn

4 cos^{2} (x) - 3 = - 1

tan (x) = 2.5

y, arctan (y) = x

2 cot (θ) - 1 = 0

tan (x) = - 1, 0 \leq x \leq 2 π

What is the general solution for cot(x)(tan(x)-1)=0 ?
The general solution for cot(x)(tan(x)-1)=0 is x= pi/4+pin