What is the general solution for cos(4x)=sin(x) ?

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

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cos(4x)=sin(x)

cos (4 x) = sin (x)

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

Solution steps

cos (4 x) = sin (x)

Rewrite using trig identities

cos (4 x) = sin (\frac{π}{2} - 4 x)

Apply trig inverse properties

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

x = \frac{π}{2} - 4 x + 2 πn : x = \frac{π + 4 πn}{10}

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

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

cos (x) = 1

cos (- 1)

sin (x) = \frac{3}{2}

sin (\frac{2 π}{4})

cos^{2} (3 0^{\circ})

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