What is the general solution for sin(5x-10)=cos(x-8) ?

The general solution for sin(5x-10)=cos(x-8) is x=(4pin+36+pi}{12},x=\frac{4pin+4+pi)/8

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sin(5x-10)=cos(x-8)

sin (5 x - 10) = cos (x - 8)

x = \frac{4 πn + 36 + π}{12}, x = \frac{4 πn + 4 + π}{8}

Solution steps

sin (5 x - 10) = cos (x - 8)

Rewrite using trig identities

sin (5 x - 10) = sin (\frac{π}{2} - (x - 8))

Apply trig inverse properties

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn, 5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn

5 x - 10 = \frac{π}{2} - (x - 8) + 2 πn : x = \frac{4 πn + 36 + π}{12}

5 x - 10 = π - (\frac{π}{2} - (x - 8)) + 2 πn : x = \frac{4 πn + 4 + π}{8}

x = \frac{4 πn + 36 + π}{12}, x = \frac{4 πn + 4 + π}{8}

sin^{2} (x) + 5 sin (x) = 3

14 + 7 cos (2 x) = 21 cos (x)

- 8 sin^{2} (θ) - 8 sin (θ) + 12 = - 5 sin (θ) + 7

cos (x) = 1 - 2 cos^{2} (x)

sin (3 x) = 0, 0 \leq x < 2 π

What is the general solution for sin(5x-10)=cos(x-8) ?
The general solution for sin(5x-10)=cos(x-8) is x=(4pin+36+pi}{12},x=\frac{4pin+4+pi)/8