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

The general solution for 2sin(4x)=1 is x= pi/(24)+(pin)/2 ,x=(5pi}{24}+\frac{pin)/2

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2sin(4x)=1

2 sin (4 x) = 1

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

Solution steps

2 sin (4 x) = 1

Divide both sides by

2

sin (4 x) = \frac{1}{2}

General solutions for

sin (4 x) = \frac{1}{2}

4 x = \frac{π}{6} + 2 πn, 4 x = \frac{5 π}{6} + 2 πn

Solve

4 x = \frac{π}{6} + 2 πn : x = \frac{π}{24} + \frac{πn}{2}

Solve

4 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{24} + \frac{πn}{2}

x = \frac{π}{24} + \frac{πn}{2}, x = \frac{5 π}{24} + \frac{πn}{2}

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

(cos (x) + 1) (cos (x) - 4) = 0

cos (10 x) = 0

7 - 5 cos (x) = 10

sin^{2} (θ) - 2 = sin (θ)

What is the general solution for 2sin(4x)=1 ?
The general solution for 2sin(4x)=1 is x= pi/(24)+(pin)/2 ,x=(5pi}{24}+\frac{pin)/2