What is the general solution for 2sin(4x)+sqrt(3)=0 ?

The general solution for 2sin(4x)+sqrt(3)=0 is x= pi/3+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2

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2sin(4x)+sqrt(3)=0

2 sin (4 x) + 3 = 0

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

Solution steps

2 sin (4 x) + 3 = 0

Move

3

to the right side

2 sin (4 x) = - 3

Divide both sides by

2

sin (4 x) = - \frac{3}{2}

General solutions for

sin (4 x) = - \frac{3}{2}

4 x = \frac{4 π}{3} + 2 πn, 4 x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

4 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{π}{3} + \frac{πn}{2}, x = \frac{5 π}{12} + \frac{πn}{2}

7 sec (x) + 7 tan (x) = 7

sin (2 x) = - 2 sin (x)

10 sec^{2} (x) + 5 tan^{2} (x) - 15 = 0

sin (2 x) + 1 = 0

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

What is the general solution for 2sin(4x)+sqrt(3)=0 ?
The general solution for 2sin(4x)+sqrt(3)=0 is x= pi/3+(pin)/2 ,x=(5pi}{12}+\frac{pin)/2