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

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

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cos(θ)+sin(θ)=1

cos (θ) + sin (θ) = 1

θ = 2 πn, θ = 2 πn + \frac{π}{2}

Solution steps

cos (θ) + sin (θ) = 1

Rewrite using trig identities

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}

2 cos (3 x) = - 1

6 sin (\frac{θ}{2}) = - 6 cos (\frac{θ}{2})

csc (θ) = - \frac{4}{3}

9 sin^{2} (θ) + 3 cos (θ) - 9 = - 2

2 cos (3 t) - 1 = 0

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