What is the general solution for sin(8x+2)=cos(6x-10) ?

The general solution for sin(8x+2)=cos(6x-10) is x=(4pin+16+pi}{28},x=\frac{pi+4pin-24)/4

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sin(8x+2)=cos(6x-10)

sin (8 x + 2) = cos (6 x - 10)

x = \frac{4 πn + 16 + π}{28}, x = \frac{π + 4 πn - 24}{4}

Solution steps

sin (8 x + 2) = cos (6 x - 10)

Rewrite using trig identities

sin (8 x + 2) = sin (\frac{π}{2} - (6 x - 10))

Apply trig inverse properties

8 x + 2 = \frac{π}{2} - (6 x - 10) + 2 πn, 8 x + 2 = π - (\frac{π}{2} - (6 x - 10)) + 2 πn

8 x + 2 = \frac{π}{2} - (6 x - 10) + 2 πn : x = \frac{4 πn + 16 + π}{28}

8 x + 2 = π - (\frac{π}{2} - (6 x - 10)) + 2 πn : x = \frac{π + 4 πn - 24}{4}

x = \frac{4 πn + 16 + π}{28}, x = \frac{π + 4 πn - 24}{4}

cos (2 θ - \frac{π}{2}) = - 1, 0 \leq θ \leq 2 π

sin^{2} (2 x) = 2 sin^{2} (x)

2 cos (x) + 2 sin (x) = 0

\frac{3}{2} = sin (arcsin (0) + c_{1})

tan^{2} (x) - sin^{2} (x) = tan^{2} (x) + sin^{2} (x)

What is the general solution for sin(8x+2)=cos(6x-10) ?
The general solution for sin(8x+2)=cos(6x-10) is x=(4pin+16+pi}{28},x=\frac{pi+4pin-24)/4