What is the general solution for sin(4x-3)=cos(5x-6) ?

The general solution for sin(4x-3)=cos(5x-6) is x=(4pin+18+pi}{18},x=-\frac{pi+4pin-6)/2

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sin(4x-3)=cos(5x-6)

sin (4 x - 3) = cos (5 x - 6)

x = \frac{4 πn + 18 + π}{18}, x = - \frac{π + 4 πn - 6}{2}

Solution steps

sin (4 x - 3) = cos (5 x - 6)

Rewrite using trig identities

sin (4 x - 3) = sin (\frac{π}{2} - (5 x - 6))

Apply trig inverse properties

4 x - 3 = \frac{π}{2} - (5 x - 6) + 2 πn, 4 x - 3 = π - (\frac{π}{2} - (5 x - 6)) + 2 πn

4 x - 3 = \frac{π}{2} - (5 x - 6) + 2 πn : x = \frac{4 πn + 18 + π}{18}

4 x - 3 = π - (\frac{π}{2} - (5 x - 6)) + 2 πn : x = - \frac{π + 4 πn - 6}{2}

x = \frac{4 πn + 18 + π}{18}, x = - \frac{π + 4 πn - 6}{2}

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

sin (x) = sin (\frac{π}{10})

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

sin (3 x) - sin (x) = - 2 sin (2 x) sin (x)

x, 0.05 cos (x) = - sin (x)

What is the general solution for sin(4x-3)=cos(5x-6) ?
The general solution for sin(4x-3)=cos(5x-6) is x=(4pin+18+pi}{18},x=-\frac{pi+4pin-6)/2