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

The general solution for sin(2x)=cos(2x)+1 is x= pi/4+pin,x=pin+pi/2

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

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

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

Solution steps

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

Subtract

cos (2 x) + 1

from both sides

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

Rewrite using trig identities

- 1 + 2 sin (2 x - \frac{π}{4}) = 0

Move

1

to the right side

2 sin (2 x - \frac{π}{4}) = 1

Divide both sides by

2

sin (2 x - \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (2 x - \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

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

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

8 sin^{2} (x) - 2 = 0

y, sin (x) = x (1 + tan (y))

sin (2 x) - sin (x) = 0, (0, 2 π)

sin^{4} (x) + cos^{4} (x) = \frac{7}{9}

tan (\frac{θ}{5}) + 3 = 0

What is the general solution for sin(2x)=cos(2x)+1 ?
The general solution for sin(2x)=cos(2x)+1 is x= pi/4+pin,x=pin+pi/2