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

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

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cos(x)=sin(4x)

cos (x) = sin (4 x)

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

Solution steps

cos (x) = sin (4 x)

Rewrite using trig identities

cos (x) = sin (\frac{π}{2} - x)

Apply trig inverse properties

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

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

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

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

0 = 2 + 4 sin (x)

sin (x) = \frac{1}{5}

cos (x) + cos (x) tan (x) = 0

4 sin^{3} (x) - sin (x) = 0

sin (θ) = 0.49

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