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

The general solution for sin(5x)=cos(3x) is x=(pi+4pin}{16},x=\frac{pi+4pin)/4

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sin(5x)=cos(3x)

sin (5 x) = cos (3 x)

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

Solution steps

sin (5 x) = cos (3 x)

Rewrite using trig identities

sin (5 x) = sin (\frac{π}{2} - 3 x)

Apply trig inverse properties

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

5 x = \frac{π}{2} - 3 x + 2 πn : x = \frac{π + 4 πn}{16}

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

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

sin^{3} (x) = \frac{1}{8}

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

cos (7 x) = - \frac{3}{2}

y, x sin (y) + cos (x) = 1

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

What is the general solution for sin(5x)=cos(3x) ?
The general solution for sin(5x)=cos(3x) is x=(pi+4pin}{16},x=\frac{pi+4pin)/4