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

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

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sin(x)=-cos(4x)

sin (x) = - cos (4 x)

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

Solution steps

sin (x) = - cos (4 x)

Multiply by

- 1

- 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}{6}

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

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

cos (θ) = \frac{2}{3 38}

sec (x) cos (x) = sin (x)

tan (θ) - 1 - 2 = sec (θ)

3 cos (2 x) + 4 cos (4 x) - 5 = 0

cos (2 θ) = \frac{20}{29}

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