What is the general solution for sin(30)=cos(2x) ?

The general solution for sin(30)=cos(2x) is x=30+180n,x=150+180n

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sin(30)=cos(2x)

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

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

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

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

\frac{1}{2} = cos (2 x)

Switch sides

cos (2 x) = \frac{1}{2}

General solutions for

cos (2 x) = \frac{1}{2}

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

Solve

2 x = 6 0^{\circ} + 36 0^{\circ} n : x = 3 0^{\circ} + 18 0^{\circ} n

Solve

2 x = 30 0^{\circ} + 36 0^{\circ} n : x = 15 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n, x = 15 0^{\circ} + 18 0^{\circ} n

tan (2 x) sin (x) - sin (x) - tan (2 x) + 1 = 0

3 sec (x) - cos (x) - 2 = 0

- 2 sin (t) = - 2

x, r^{2} = sin (2 x)

3 cos (3 t) = 0

What is the general solution for sin(30)=cos(2x) ?
The general solution for sin(30)=cos(2x) is x=30+180n,x=150+180n