What is the general solution for sin(5x-28)=cos(3x-50) ?

The general solution for sin(5x-28)=cos(3x-50) is x=(4pin+156+pi}{16},x=\frac{pi+4pin-44)/4

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sin(5x-28)=cos(3x-50)

sin (5 x - 28) = cos (3 x - 50)

x = \frac{4 πn + 156 + π}{16}, x = \frac{π + 4 πn - 44}{4}

Solution steps

sin (5 x - 28) = cos (3 x - 50)

Rewrite using trig identities

sin (5 x - 28) = sin (\frac{π}{2} - (3 x - 50))

Apply trig inverse properties

5 x - 28 = \frac{π}{2} - (3 x - 50) + 2 πn, 5 x - 28 = π - (\frac{π}{2} - (3 x - 50)) + 2 πn

5 x - 28 = \frac{π}{2} - (3 x - 50) + 2 πn : x = \frac{4 πn + 156 + π}{16}

5 x - 28 = π - (\frac{π}{2} - (3 x - 50)) + 2 πn : x = \frac{π + 4 πn - 44}{4}

x = \frac{4 πn + 156 + π}{16}, x = \frac{π + 4 πn - 44}{4}

sin (x) - 1 - 3 sin^{2} (x) = 0

2 cos^{2} (x) + 2 cos (x) - 3 = 0

sec^{2} (x) cot (x) = 8, 0 < x < π

tan (x) = \frac{1.5}{2}

3 csc^{2} (x) - 5 csc (x) = 2

What is the general solution for sin(5x-28)=cos(3x-50) ?
The general solution for sin(5x-28)=cos(3x-50) is x=(4pin+156+pi}{16},x=\frac{pi+4pin-44)/4