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

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

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

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

x = πn, x = πn + \frac{π}{4}

Solution steps

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

Rewrite using trig identities

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 = πn

Solve

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

x = πn, x = πn + \frac{π}{4}

θ, sin (θ) = \frac{1}{2}

sin (x + \frac{3 π}{2}) - cos^{2} (x) = 0

6 cos (x) - 6 sin (x) = 0

3 tan^{3} (x) - tan (x) = 0

5 sin (x) + 12 cos (x) = 13

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