What is the general solution for sqrt(2)sin(2x)=1,0<= x<= 2pi ?

The general solution for sqrt(2)sin(2x)=1,0<= x<= 2pi is x= pi/8 ,x=(3pi)/8 ,x=(9pi)/8 ,x=(11pi)/8

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sqrt(2)sin(2x)=1,0<= x<= 2pi

2 sin (2 x) = 1, 0 \leq x \leq 2 π

x = \frac{π}{8}, x = \frac{3 π}{8}, x = \frac{9 π}{8}, x = \frac{11 π}{8}

Solution steps

2 sin (2 x) = 1, 0 \leq x \leq 2 π

Divide both sides by

2

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

General solutions for

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

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

Solve

2 x = \frac{π}{4} + 2 πn : x = \frac{π}{8} + πn

Solve

2 x = \frac{3 π}{4} + 2 πn : x = \frac{3 π}{8} + πn

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

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{8}, x = \frac{3 π}{8}, x = \frac{9 π}{8}, x = \frac{11 π}{8}

cos (2 x) = 4

- sin (θ) - sin (2 θ) = 0

cos (\frac{π}{2} + x) = sin (x)

cot (θ) = 1.5

- 1 = 2 sin (x)

What is the general solution for sqrt(2)sin(2x)=1,0<= x<= 2pi ?
The general solution for sqrt(2)sin(2x)=1,0<= x<= 2pi is x= pi/8 ,x=(3pi)/8 ,x=(9pi)/8 ,x=(11pi)/8