What is the general solution for cos(7x)=sin(5x-6) ?

The general solution for cos(7x)=sin(5x-6) is x=(12+4pin+pi}{24},x=-\frac{pi+4pin+12)/4

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cos(7x)=sin(5x-6)

cos (7 x) = sin (5 x - 6)

x = \frac{12 + 4 πn + π}{24}, x = - \frac{π + 4 πn + 12}{4}

Solution steps

cos (7 x) = sin (5 x - 6)

Rewrite using trig identities

cos (7 x) = sin (\frac{π}{2} - 7 x)

Apply trig inverse properties

5 x - 6 = \frac{π}{2} - 7 x + 2 πn, 5 x - 6 = π - (\frac{π}{2} - 7 x) + 2 πn

5 x - 6 = \frac{π}{2} - 7 x + 2 πn : x = \frac{12 + 4 πn + π}{24}

5 x - 6 = π - (\frac{π}{2} - 7 x) + 2 πn : x = - \frac{π + 4 πn + 12}{4}

x = \frac{12 + 4 πn + π}{24}, x = - \frac{π + 4 πn + 12}{4}

100 = 211.49 - 20.96 cosh (0.03291765 x)

3 sec^{2} (x) + 4 cos^{2} (x) = 7

cos (θ) = \frac{43}{90}

8 cos (2 x - 5) = 3

\frac{116}{sin ( 9 0 ^{\circ} )} = \frac{4}{sin ( x )}

What is the general solution for cos(7x)=sin(5x-6) ?
The general solution for cos(7x)=sin(5x-6) is x=(12+4pin+pi}{24},x=-\frac{pi+4pin+12)/4