What is the general solution for tan(X)cot(X)-tan(X)+2cot(X)=0 ?

The general solution for tan(X)cot(X)-tan(X)+2cot(X)=0 is X=1.10714…+pin,X=(3pi)/4+pin

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tan(X)cot(X)-tan(X)+2cot(X)=0

tan (X) cot (X) - tan (X) + 2 cot (X) = 0

X = 1.10714 \dots + πn, X = \frac{3 π}{4} + πn

Solution steps

tan (X) cot (X) - tan (X) + 2 cot (X) = 0

Rewrite using trig identities

1 - \frac{1}{cot ( X )} + 2 cot (X) = 0

Solve by substitution

cot (X) = \frac{1}{2}, cot (X) = - 1

cot (X) = \frac{1}{2} : X = arccot (\frac{1}{2}) + πn

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

Combine all the solutions

X = arccot (\frac{1}{2}) + πn, X = \frac{3 π}{4} + πn

Show solutions in decimal form

X = 1.10714 \dots + πn, X = \frac{3 π}{4} + πn

sin (x) = - 0.3926

(sin (2 x) + 1) = 0, 0^{\circ} \leq x < 36 0^{\circ}

4 sin (x) + 2 = 2 sin (x)

y, - \frac{1}{2} cot (y) = \frac{t ^{2}}{2} + C

4 cos (2 t) + 1 = 3, 0, \frac{π}{2}

What is the general solution for tan(X)cot(X)-tan(X)+2cot(X)=0 ?
The general solution for tan(X)cot(X)-tan(X)+2cot(X)=0 is X=1.10714…+pin,X=(3pi)/4+pin