What is the general solution for sin(4x-22)=cos(6x-13) ?

The general solution for sin(4x-22)=cos(6x-13) is x=(4pin+70+pi}{20},x=-\frac{4pin+18+pi)/4

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sin(4x-22)=cos(6x-13)

sin (4 x - 22) = cos (6 x - 13)

x = \frac{4 πn + 70 + π}{20}, x = - \frac{4 πn + 18 + π}{4}

Solution steps

sin (4 x - 22) = cos (6 x - 13)

Rewrite using trig identities

sin (4 x - 22) = sin (\frac{π}{2} - (6 x - 13))

Apply trig inverse properties

4 x - 22 = \frac{π}{2} - (6 x - 13) + 2 πn, 4 x - 22 = π - (\frac{π}{2} - (6 x - 13)) + 2 πn

4 x - 22 = \frac{π}{2} - (6 x - 13) + 2 πn : x = \frac{4 πn + 70 + π}{20}

4 x - 22 = π - (\frac{π}{2} - (6 x - 13)) + 2 πn : x = - \frac{4 πn + 18 + π}{4}

x = \frac{4 πn + 70 + π}{20}, x = - \frac{4 πn + 18 + π}{4}

cos (2 x) + 1 = 2

csc (x) = - \frac{3}{5}

cos (x) = \frac{3}{5}, cos (2 π + x)

sin (4 5^{\circ}) = 1.57 \cdot sin (θ)

\frac{2}{3} = sec (x)

What is the general solution for sin(4x-22)=cos(6x-13) ?
The general solution for sin(4x-22)=cos(6x-13) is x=(4pin+70+pi}{20},x=-\frac{4pin+18+pi)/4