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

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

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sin(α)+cos(α)=1

sin (α) + cos (α) = 1

α = 2 πn, α = 2 πn + \frac{π}{2}

Solution steps

sin (α) + cos (α) = 1

Rewrite using trig identities

2 sin (α + \frac{π}{4}) = 1

Divide both sides by

2

sin (α + \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (α + \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

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

α = 2 πn, α = 2 πn + \frac{π}{2}

2 sin (θ) = 3 tan (θ)

sin (x^{2} - 1) = 4

1 - cos (x) = \frac{2 π}{3}

sin (A) = \frac{1}{3}

sin (θ) = - 0.78

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