What is the general solution for sin(x-4)=cos(9x+4) ?

The general solution for sin(x-4)=cos(9x+4) is x=(4pin+pi)/(20),x=-(4pin+16+pi)/(16)

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sin(x-4)=cos(9x+4)

sin (x - 4) = cos (9 x + 4)

x = \frac{4 πn + π}{20}, x = - \frac{4 πn + 16 + π}{16}

Solution steps

sin (x - 4) = cos (9 x + 4)

Rewrite using trig identities

sin (x - 4) = sin (\frac{π}{2} - (9 x + 4))

Apply trig inverse properties

x - 4 = \frac{π}{2} - (9 x + 4) + 2 πn, x - 4 = π - (\frac{π}{2} - (9 x + 4)) + 2 πn

x - 4 = \frac{π}{2} - (9 x + 4) + 2 πn : x = \frac{4 πn + π}{20}

x - 4 = π - (\frac{π}{2} - (9 x + 4)) + 2 πn : x = - \frac{4 πn + 16 + π}{16}

x = \frac{4 πn + π}{20}, x = - \frac{4 πn + 16 + π}{16}

x, 0 = - 2 sin (x) - 4 cos (2 x)

tan (a) = \frac{4}{4}

cos^{2} (θ) = 2 cos (θ)

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

2 cos^{2} (x) + cos (2 x) - 2 = 0

What is the general solution for sin(x-4)=cos(9x+4) ?
The general solution for sin(x-4)=cos(9x+4) is x=(4pin+pi)/(20),x=-(4pin+16+pi)/(16)