What is the general solution for sin(30)=cos(x-20) ?

The general solution for sin(30)=cos(x-20) is x=360n+80,x=360n+320

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sin(30)=cos(x-20)

sin (3 0^{\circ}) = cos (x - 2 0^{\circ})

x = 36 0^{\circ} n + 8 0^{\circ}, x = 36 0^{\circ} n + 32 0^{\circ}

Solution steps

sin (3 0^{\circ}) = cos (x - 2 0^{\circ})

sin (3 0^{\circ}) = \frac{1}{2}

\frac{1}{2} = cos (x - 2 0^{\circ})

Switch sides

cos (x - 2 0^{\circ}) = \frac{1}{2}

General solutions for

cos (x - 2 0^{\circ}) = \frac{1}{2}

x - 2 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n, x - 2 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n

Solve

x - 2 0^{\circ} = 6 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 8 0^{\circ}

Solve

x - 2 0^{\circ} = 30 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 32 0^{\circ}

x = 36 0^{\circ} n + 8 0^{\circ}, x = 36 0^{\circ} n + 32 0^{\circ}

- 7 sin (x) = 0

2 sin^{2} (x) - 1 = 0, 0 \leq x < 2 π

tan^{2} (x) + 2 tan (x) = - 1

4 csc^{2} (x) - 2 = 0

sin (2 θ - \frac{π}{2}) = - 1, 0 \leq θ < 2 π

What is the general solution for sin(30)=cos(x-20) ?
The general solution for sin(30)=cos(x-20) is x=360n+80,x=360n+320