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

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

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sin(x)=cos(4x)

sin (x) = cos (4 x)

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

Solution steps

sin (x) = cos (4 x)

Rewrite using trig identities

sin (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) = \frac{13}{12}

- 2 + cot (θ) = - 3

sin^{2} (x) + sin (x) = 0, 0 \leq x \leq 2 π

\frac{1}{tan ( x )} = - 1

64 cosh^{4} (x) - 64 cosh^{2} (x) - 9 = 0

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