What is the general solution for sin(2x)=cos(x-60) ?

The general solution for sin(2x)=cos(x-60) is x=(2160n+900)/(18),x=180-150+360n

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sin(2x)=cos(x-60)

sin (2 x) = cos (x - 6 0^{\circ})

x = \frac{216 0 ^{\circ} n + 90 0 ^{\circ}}{18}, x = 18 0^{\circ} - 15 0^{\circ} + 36 0^{\circ} n

Solution steps

sin (2 x) = cos (x - 6 0^{\circ})

Rewrite using trig identities

sin (2 x) = sin (9 0^{\circ} - (x - 6 0^{\circ}))

Apply trig inverse properties

2 x = 9 0^{\circ} - (x - 6 0^{\circ}) + 36 0^{\circ} n, 2 x = 18 0^{\circ} - (9 0^{\circ} - (x - 6 0^{\circ})) + 36 0^{\circ} n

2 x = 9 0^{\circ} - (x - 6 0^{\circ}) + 36 0^{\circ} n : x = \frac{216 0 ^{\circ} n + 90 0 ^{\circ}}{18}

2 x = 18 0^{\circ} - (9 0^{\circ} - (x - 6 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} - 15 0^{\circ} + 36 0^{\circ} n

x = \frac{216 0 ^{\circ} n + 90 0 ^{\circ}}{18}, x = 18 0^{\circ} - 15 0^{\circ} + 36 0^{\circ} n

tan (18 0^{\circ} - θ) = 33

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

arccsc (2 x) = \frac{π}{6}

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

sin (\frac{1}{2} x) = - 1

What is the general solution for sin(2x)=cos(x-60) ?
The general solution for sin(2x)=cos(x-60) is x=(2160n+900)/(18),x=180-150+360n