What is the general solution for 2cot(x)+csc(x)=0 ?

The general solution for 2cot(x)+csc(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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2cot(x)+csc(x)=0

2 cot (x) + csc (x) = 0

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

2 cot (x) + csc (x) = 0

Express with sin, cos

\frac{1 + 2 cos ( x )}{sin ( x )} = 0

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

1 + 2 cos (x) = 0

Move

1

to the right side

2 cos (x) = - 1

Divide both sides by

2

cos (x) = - \frac{1}{2}

General solutions for

cos (x) = - \frac{1}{2}

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

sin (x) = - 0.15

74 = 58 cos (x) + 71 sin (x)

sin (\frac{1}{x}) = - 1

5 sin (x) + 4 = 0

cos^{2} (\frac{x}{2}) = 0

What is the general solution for 2cot(x)+csc(x)=0 ?
The general solution for 2cot(x)+csc(x)=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin