What is the general solution for cos(6x)=sin(x-1) ?

The general solution for cos(6x)=sin(x-1) is x=(2+4pin+pi)/(14),x=-(pi+4pin+2)/(10)

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cos(6x)=sin(x-1)

cos (6 x) = sin (x - 1)

x = \frac{2 + 4 πn + π}{14}, x = - \frac{π + 4 πn + 2}{10}

Solution steps

cos (6 x) = sin (x - 1)

Rewrite using trig identities

cos (6 x) = sin (\frac{π}{2} - 6 x)

Apply trig inverse properties

x - 1 = \frac{π}{2} - 6 x + 2 πn, x - 1 = π - (\frac{π}{2} - 6 x) + 2 πn

x - 1 = \frac{π}{2} - 6 x + 2 πn : x = \frac{2 + 4 πn + π}{14}

x - 1 = π - (\frac{π}{2} - 6 x) + 2 πn : x = - \frac{π + 4 πn + 2}{10}

x = \frac{2 + 4 πn + π}{14}, x = - \frac{π + 4 πn + 2}{10}

tan (θ) = \frac{72}{65}

cos (x) + cos (\frac{x}{2}) + 1 = 0

sin (x - 1) = sin (x)

sin (θ) = \frac{1.5}{2}

- cos (θ) = cos (θ)

What is the general solution for cos(6x)=sin(x-1) ?
The general solution for cos(6x)=sin(x-1) is x=(2+4pin+pi)/(14),x=-(pi+4pin+2)/(10)