What is the general solution for csc(3x)=2 ?

The general solution for csc(3x)=2 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3

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csc(3x)=2

csc (3 x) = 2

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{5 π}{18} + \frac{2 πn}{3}

Solution steps

csc (3 x) = 2

General solutions for

csc (3 x) = 2

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{5 π}{6} + 2 πn

Solve

3 x = \frac{π}{6} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{5 π}{18} + \frac{2 πn}{3}

2 cos (x) + sec (x) = 3

cos^{2} (2 x) = 0

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

2 cos (x) - sin (2 x) = 0

4 sin^{2} (x) - 1 = 0, 0 \leq x \leq \frac{π}{2}

What is the general solution for csc(3x)=2 ?
The general solution for csc(3x)=2 is x= pi/(18)+(2pin)/3 ,x=(5pi}{18}+\frac{2pin)/3