What is the general solution for sin(5x+8)=cos(9x-16) ?

The general solution for sin(5x+8)=cos(9x-16) is x=(4pin+16+pi}{28},x=-\frac{pi+4pin-48)/8

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sin(5x+8)=cos(9x-16)

sin (5 x + 8) = cos (9 x - 16)

x = \frac{4 πn + 16 + π}{28}, x = - \frac{π + 4 πn - 48}{8}

Solution steps

sin (5 x + 8) = cos (9 x - 16)

Rewrite using trig identities

sin (5 x + 8) = sin (\frac{π}{2} - (9 x - 16))

Apply trig inverse properties

5 x + 8 = \frac{π}{2} - (9 x - 16) + 2 πn, 5 x + 8 = π - (\frac{π}{2} - (9 x - 16)) + 2 πn

5 x + 8 = \frac{π}{2} - (9 x - 16) + 2 πn : x = \frac{4 πn + 16 + π}{28}

5 x + 8 = π - (\frac{π}{2} - (9 x - 16)) + 2 πn : x = - \frac{π + 4 πn - 48}{8}

x = \frac{4 πn + 16 + π}{28}, x = - \frac{π + 4 πn - 48}{8}

cos (x^{\circ}) = \frac{125}{174}

csc (θ) = 23

2 csc^{2} (x) + 5 cot (x) = 5

60 sin (4 5^{\circ}) = 400 sin (θ)

(1 + tan (x)) (5 sin (x) - 2) = 0

What is the general solution for sin(5x+8)=cos(9x-16) ?
The general solution for sin(5x+8)=cos(9x-16) is x=(4pin+16+pi}{28},x=-\frac{pi+4pin-48)/8