What is the general solution for cos(3x)=sin(x-30) ?

The general solution for cos(3x)=sin(x-30) is x=(180(3n+1))/6 ,x=-(180(3n+1))/3

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cos(3x)=sin(x-30)

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

x = \frac{18 0 ^{\circ} ( 3 n + 1 )}{6}, x = - \frac{18 0 ^{\circ} ( 3 n + 1 )}{3}

Solution steps

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

Rewrite using trig identities

cos (3 x) = sin (9 0^{\circ} - 3 x)

Apply trig inverse properties

x - 3 0^{\circ} = 9 0^{\circ} - 3 x + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n

x - 3 0^{\circ} = 9 0^{\circ} - 3 x + 36 0^{\circ} n : x = \frac{18 0 ^{\circ} ( 3 n + 1 )}{6}

x - 3 0^{\circ} = 18 0^{\circ} - (9 0^{\circ} - 3 x) + 36 0^{\circ} n : x = - \frac{18 0 ^{\circ} ( 3 n + 1 )}{3}

x = \frac{18 0 ^{\circ} ( 3 n + 1 )}{6}, x = - \frac{18 0 ^{\circ} ( 3 n + 1 )}{3}

4 sin (θ) = 4 cos (2 θ)

tan (5 θ + 30) = 1

885 cos (θ) - 70 = cos (25 0^{\circ})

tan (x) + 5 = 0, x \leq 0 < 2 π

\frac{31.5}{sin ( 57.2 2 ^{\circ} )} = \frac{24.4}{sin ( x )}

What is the general solution for cos(3x)=sin(x-30) ?
The general solution for cos(3x)=sin(x-30) is x=(180(3n+1))/6 ,x=-(180(3n+1))/3