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

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

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cos(θ)=1+sin(θ)

cos (θ) = 1 + sin (θ)

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

Solution steps

cos (θ) = 1 + sin (θ)

Subtract

1 + sin (θ)

from both sides

cos (θ) - 1 - sin (θ) = 0

Rewrite using trig identities

- 1 - 2 sin (\frac{4 θ - π}{4}) = 0

Move

1

to the right side

- 2 sin (\frac{4 θ - π}{4}) = 1

Divide both sides by

- 2

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

General solutions for

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

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

Solve

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

Solve

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

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

4 sin^{2} (x) - 7 sin (x) - 2 = 0

cos (x) = - sin (2 x)

3 cot (x) - 3 = 0

cot (3 x) = \frac{3}{3}, 0 \leq x \leq 2 π

csc^{2} (θ) + 7 csc (θ) + 12 = 0

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