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

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

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sin(α)+1=cos(α)

sin (α) + 1 = cos (α)

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

Solution steps

sin (α) + 1 = cos (α)

Subtract

cos (α)

from both sides

sin (α) + 1 - cos (α) = 0

Rewrite using trig identities

1 + 2 sin (α - \frac{π}{4}) = 0

Move

1

to the right side

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{5 π}{4} + 2 πn, α - \frac{π}{4} = \frac{7 π}{4} + 2 πn

Solve

α - \frac{π}{4} = \frac{5 π}{4} + 2 πn : α = 2 πn + \frac{3 π}{2}

Solve

α - \frac{π}{4} = \frac{7 π}{4} + 2 πn : α = 2 πn + 2 π

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

\frac{sin ( 11 5 ^{\circ} )}{53} = \frac{sin ( S )}{83}

2 cos (x) - tan (x) = 0

0 = 3 sin (x)

sin (\frac{θ}{2}) = 0.4

arccos (x) = \frac{79}{9 70}

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