What is the general solution for 2sin(4x)+6=5 ?

The general solution for 2sin(4x)+6=5 is x=(7pi}{24}+(pin)/2 ,x=(11pi)/(24)+\frac{pin)/2

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2sin(4x)+6=5

2 sin (4 x) + 6 = 5

x = \frac{7 π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

Solution steps

2 sin (4 x) + 6 = 5

Move

6

to the right side

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{7 π}{6} + 2 πn, 4 x = \frac{11 π}{6} + 2 πn

Solve

4 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{24} + \frac{πn}{2}

Solve

4 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{24} + \frac{πn}{2}

x = \frac{7 π}{24} + \frac{πn}{2}, x = \frac{11 π}{24} + \frac{πn}{2}

7 sin (x) tan (x) = - 8 tan (x)

sin^{2} (x) + 2 sin (x) - 3 = 0

sin^{2} (x) - tan (x) cos^{2} (x) = 0

2 sin (x) cos (x) - sin (x) + 2 cos (x) - 1 = 0

sec^{2} (x) = 2 tan (x)

What is the general solution for 2sin(4x)+6=5 ?
The general solution for 2sin(4x)+6=5 is x=(7pi}{24}+(pin)/2 ,x=(11pi)/(24)+\frac{pin)/2