What is the general solution for (sec(3x)-sqrt(2))(tan(2x)-1)=0 ?

The general solution for (sec(3x)-sqrt(2))(tan(2x)-1)=0 is x= pi/8+(pin)/2

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(sec(3x)-sqrt(2))(tan(2x)-1)=0

(sec (3 x) - 2) (tan (2 x) - 1) = 0

x = \frac{π}{8} + \frac{πn}{2}

Solution steps

(sec (3 x) - 2) (tan (2 x) - 1) = 0

Solving each part separately

sec (3 x) - 2 = 0 or tan (2 x) - 1 = 0

sec (3 x) - 2 = 0 : x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}

tan (2 x) - 1 = 0 : x = \frac{π}{8} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{12} + \frac{2 πn}{3}, x = \frac{7 π}{12} + \frac{2 πn}{3}, x = \frac{π}{8} + \frac{πn}{2}

Since the equation is undefined for:

\frac{π}{12} + \frac{2 πn}{3}, \frac{7 π}{12} + \frac{2 πn}{3}

x = \frac{π}{8} + \frac{πn}{2}

cos (2 x) \cdot 2 - 2 cos (x) = 0

- 2 sin (2 x) = \frac{π}{12}

cos (x) = \frac{sec ( x )}{4}

sin (10 x) = sin (10 (x + 1))

sin^{2} (θ) + 3 sin (θ) = 0

What is the general solution for (sec(3x)-sqrt(2))(tan(2x)-1)=0 ?
The general solution for (sec(3x)-sqrt(2))(tan(2x)-1)=0 is x= pi/8+(pin)/2