What is the general solution for cos(10x)=sin(5x-3) ?

The general solution for cos(10x)=sin(5x-3) is x=(6+4pin+pi)/(30),x=-(pi+4pin+6)/(10)

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cos(10x)=sin(5x-3)

cos (10 x) = sin (5 x - 3)

x = \frac{6 + 4 πn + π}{30}, x = - \frac{π + 4 πn + 6}{10}

Solution steps

cos (10 x) = sin (5 x - 3)

Rewrite using trig identities

cos (10 x) = sin (\frac{π}{2} - 10 x)

Apply trig inverse properties

5 x - 3 = \frac{π}{2} - 10 x + 2 πn, 5 x - 3 = π - (\frac{π}{2} - 10 x) + 2 πn

5 x - 3 = \frac{π}{2} - 10 x + 2 πn : x = \frac{6 + 4 πn + π}{30}

5 x - 3 = π - (\frac{π}{2} - 10 x) + 2 πn : x = - \frac{π + 4 πn + 6}{10}

x = \frac{6 + 4 πn + π}{30}, x = - \frac{π + 4 πn + 6}{10}

13 tan (a) = 10, 0 b = 100

- 4 cos (3 x) = 0

\frac{sin ( 4 0 ^{\circ} )}{8} = \frac{sin ( 65.3 8 ^{\circ} )}{sin ( x )}

cos (28 π + x) = \frac{1}{2}

1 - tan^{2} (x) = \frac{cos ^{2} ( x )}{cos ^{2} ( x )}

What is the general solution for cos(10x)=sin(5x-3) ?
The general solution for cos(10x)=sin(5x-3) is x=(6+4pin+pi)/(30),x=-(pi+4pin+6)/(10)