What is the general solution for sin(3x+5)=cos(4x+1) ?

The general solution for sin(3x+5)=cos(4x+1) is x=(4pin+pi-12}{14},x=-\frac{pi+4pin-8)/2

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sin(3x+5)=cos(4x+1)

sin (3 x + 5) = cos (4 x + 1)

x = \frac{4 πn + π - 12}{14}, x = - \frac{π + 4 πn - 8}{2}

Solution steps

sin (3 x + 5) = cos (4 x + 1)

Rewrite using trig identities

sin (3 x + 5) = sin (\frac{π}{2} - (4 x + 1))

Apply trig inverse properties

3 x + 5 = \frac{π}{2} - (4 x + 1) + 2 πn, 3 x + 5 = π - (\frac{π}{2} - (4 x + 1)) + 2 πn

3 x + 5 = \frac{π}{2} - (4 x + 1) + 2 πn : x = \frac{4 πn + π - 12}{14}

3 x + 5 = π - (\frac{π}{2} - (4 x + 1)) + 2 πn : x = - \frac{π + 4 πn - 8}{2}

x = \frac{4 πn + π - 12}{14}, x = - \frac{π + 4 πn - 8}{2}

6 sin^{2} (θ) - 3 = 0

4 cos (x) - 4 sin (x) = 26

sin (x) = \frac{8}{9}

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

sin (θ) + sin (2 θ) = 0

What is the general solution for sin(3x+5)=cos(4x+1) ?
The general solution for sin(3x+5)=cos(4x+1) is x=(4pin+pi-12}{14},x=-\frac{pi+4pin-8)/2