What is the general solution for cos(3x)+sin(3x)=1 ?

The general solution for cos(3x)+sin(3x)=1 is x=(2pin)/3 ,x=(2pin)/3+pi/6

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cos(3x)+sin(3x)=1

cos (3 x) + sin (3 x) = 1

x = \frac{2 πn}{3}, x = \frac{2 πn}{3} + \frac{π}{6}

Solution steps

cos (3 x) + sin (3 x) = 1

Rewrite using trig identities

2 sin (3 x + \frac{π}{4}) = 1

Divide both sides by

2

sin (3 x + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (3 x + \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

3 x + \frac{π}{4} = \frac{3 π}{4} + 2 πn : x = \frac{2 πn}{3} + \frac{π}{6}

x = \frac{2 πn}{3}, x = \frac{2 πn}{3} + \frac{π}{6}

3 csc (2 x) = - 2

cos (3 x) = 4 cos (3 x) - 3 cos (x)

8 arctan (x) = 2 π

sin^{2} (θ) - 1 = cos^{2} (θ)

sin (\frac{1}{x}) = 0, 5

What is the general solution for cos(3x)+sin(3x)=1 ?
The general solution for cos(3x)+sin(3x)=1 is x=(2pin)/3 ,x=(2pin)/3+pi/6