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

The general solution for cot(x)=tan(x) is x= pi/4+pin,x=(3pi)/4+pin

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cot(x)=tan(x)

cot (x) = tan (x)

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

Solution steps

cot (x) = tan (x)

Subtract

tan (x)

from both sides

cot (x) - tan (x) = 0

Rewrite using trig identities

cot (x) - \frac{1}{cot ( x )} = 0

Solve by substitution

cot (x) = 1, cot (x) = - 1

cot (x) = 1 : x = \frac{π}{4} + πn

cot (x) = - 1 : x = \frac{3 π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

2 sin^{2} (x) + 3 = 0

3 tan (\frac{x}{2}) - 3 = 0

sin^{2} (x) = \frac{3}{2}

8 cos^{2} (x) + 10 cos (x) + 3 = 0

sin (3 x) = 1, 0 \leq x < 2 π

What is the general solution for cot(x)=tan(x) ?
The general solution for cot(x)=tan(x) is x= pi/4+pin,x=(3pi)/4+pin