What is the general solution for sqrt(2)sin(4x)-1=0 ?

The general solution for sqrt(2)sin(4x)-1=0 is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2

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sqrt(2)sin(4x)-1=0

2 sin (4 x) - 1 = 0

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

Solution steps

2 sin (4 x) - 1 = 0

Move

1

to the right side

2 sin (4 x) = 1

Divide both sides by

2

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

General solutions for

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

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

Solve

4 x = \frac{π}{4} + 2 πn : x = \frac{π}{16} + \frac{πn}{2}

Solve

4 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{16} + \frac{πn}{2}

x = \frac{π}{16} + \frac{πn}{2}, x = \frac{3 π}{16} + \frac{πn}{2}

cot (θ) = 0.75

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

3 - 3 sin (x) = 6 cos^{2} (x)

- 2 tan^{2} (θ) + 2 tan (θ) + 1 = 3 tan (θ)

cos (x) = \frac{60}{61}, tan (x) = \frac{11}{60}

What is the general solution for sqrt(2)sin(4x)-1=0 ?
The general solution for sqrt(2)sin(4x)-1=0 is x= pi/(16)+(pin)/2 ,x=(3pi}{16}+\frac{pin)/2