What is the general solution for 1/(cot^2(x))+sqrt(3)tan(x)=0 ?

The general solution for 1/(cot^2(x))+sqrt(3)tan(x)=0 is x=(2pi)/3+pin

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1/(cot^2(x))+sqrt(3)tan(x)=0

\frac{1}{cot ^{2} ( x )} + 3 tan (x) = 0

x = \frac{2 π}{3} + πn

Solution steps

\frac{1}{cot ^{2} ( x )} + 3 tan (x) = 0

Simplify

\frac{1}{cot ^{2} ( x )} + 3 tan (x) : \frac{1 + 3 cot ^{2} ( x ) tan ( x )}{cot ^{2} ( x )}

\frac{1 + 3 cot ^{2} ( x ) tan ( x )}{cot ^{2} ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 + 3 cot^{2} (x) tan (x) = 0

Rewrite using trig identities

1 + cot (x) 3 = 0

Move

1

to the right side

cot (x) 3 = - 1

Divide both sides by

3

cot (x) = - \frac{3}{3}

General solutions for

cot (x) = - \frac{3}{3}

x = \frac{2 π}{3} + πn

tan (x) = 0.23

tan (x) = 0.45

2 cos (x) - 1 = sec (x)

2 - cos (x) = 2 + sin (x)

4 cos^{4} (x) - 2 cos^{3} (x) - 4 cos^{2} (x) + cos (x) + 1 = 0

What is the general solution for 1/(cot^2(x))+sqrt(3)tan(x)=0 ?
The general solution for 1/(cot^2(x))+sqrt(3)tan(x)=0 is x=(2pi)/3+pin