What is the general solution for sin(x+5)=cos(2x-2) ?

The general solution for sin(x+5)=cos(2x-2) is x=(4pin+pi-6)/6 ,x=-(pi+4pin-14)/2

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sin(x+5)=cos(2x-2)

sin (x + 5) = cos (2 x - 2)

x = \frac{4 πn + π - 6}{6}, x = - \frac{π + 4 πn - 14}{2}

Solution steps

sin (x + 5) = cos (2 x - 2)

Rewrite using trig identities

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

Apply trig inverse properties

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

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

x + 5 = π - (\frac{π}{2} - (2 x - 2)) + 2 πn : x = - \frac{π + 4 πn - 14}{2}

x = \frac{4 πn + π - 6}{6}, x = - \frac{π + 4 πn - 14}{2}

θ, z \cdot p \cdot cos (θ) = n

tan (θ) = \frac{1}{5}, csc (θ)

6 = tan (6 C)

\frac{3}{4} = tan (x)

cos (x) = - 3 + \frac{4}{cos ( x )}

What is the general solution for sin(x+5)=cos(2x-2) ?
The general solution for sin(x+5)=cos(2x-2) is x=(4pin+pi-6)/6 ,x=-(pi+4pin-14)/2