What is the general solution for sin(2x-10)=cos(x+10) ?

The general solution for sin(2x-10)=cos(x+10) is x=(3240n+720+90)/(27),x=180-80+360n+10

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sin(2x-10)=cos(x+10)

sin (2 x - 10) = cos (x + 1 0^{\circ})

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}, x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

Solution steps

sin (2 x - 10) = cos (x + 1 0^{\circ})

Rewrite using trig identities

sin (2 x - 10) = sin (9 0^{\circ} - (x + 1 0^{\circ}))

Apply trig inverse properties

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n, 2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n

2 x - 10 = 9 0^{\circ} - (x + 1 0^{\circ}) + 36 0^{\circ} n : x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}

2 x - 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 1 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

x = \frac{324 0 ^{\circ} n + 72 0 ^{\circ} + 90}{27}, x = 18 0^{\circ} - 8 0^{\circ} + 36 0^{\circ} n + 10

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What is the general solution for sin(2x-10)=cos(x+10) ?
The general solution for sin(2x-10)=cos(x+10) is x=(3240n+720+90)/(27),x=180-80+360n+10