What is the general solution for (sqrt(2/2))(cos(θ)+sin(θ))=1 ?

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

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(sqrt(2/2))(cos(θ)+sin(θ))=1

(\frac{2}{2}) (cos (θ) + sin (θ)) = 1

θ = 2 πn, θ = 2 πn + \frac{π}{2}

Solution steps

(\frac{2}{2}) (cos (θ) + sin (θ)) = 1

Rewrite using trig identities

\frac{2}{2} 2 sin (θ + \frac{π}{4}) = 1

Simplify

\frac{2}{2} 2 : 2

2 sin (θ + \frac{π}{4}) = 1

Divide both sides by

2

sin (θ + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (θ + \frac{π}{4}) = \frac{2}{2}

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

Solve

θ + \frac{π}{4} = \frac{π}{4} + 2 πn : θ = 2 πn

Solve

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

θ = 2 πn, θ = 2 πn + \frac{π}{2}

arcsin (6 x) + arcsin (6 3 x) = - \frac{π}{2}

2 cos^{2} (x) + sin (x) = 0

2 cos^{2} (x) + sin (x) = 5

x, Y = 0.5 sin (3.07 x - 2.4 t + 0.59)

\frac{( 1 + tan ( x ) )}{sec ( x )} = 2, x

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