What is the general solution for cos(3x)=-sin(x+pi/6) ?

The general solution for cos(3x)=-sin(x+pi/6) is x=(pi(3n+1))/3 ,x=-(pi(3n+1))/6

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cos(3x)=-sin(x+pi/6)

cos (3 x) = - sin (x + \frac{π}{6})

x = \frac{π ( 3 n + 1 )}{3}, x = - \frac{π ( 3 n + 1 )}{6}

Solution steps

cos (3 x) = - sin (x + \frac{π}{6})

Rewrite using trig identities

cos (3 x) = sin (\frac{π}{2} - 3 x)

Apply trig inverse properties

- (x + \frac{π}{6}) = \frac{π}{2} - 3 x + 2 πn, - (x + \frac{π}{6}) = π - (\frac{π}{2} - 3 x) + 2 πn

- (x + \frac{π}{6}) = \frac{π}{2} - 3 x + 2 πn : x = \frac{π ( 3 n + 1 )}{3}

- (x + \frac{π}{6}) = π - (\frac{π}{2} - 3 x) + 2 πn : x = - \frac{π ( 3 n + 1 )}{6}

x = \frac{π ( 3 n + 1 )}{3}, x = - \frac{π ( 3 n + 1 )}{6}

sin (θ) = \frac{7}{10}

tan (5 x) = 1

sec (5 x) = 2

5 sin (θ) - 1 = 3 sin (θ)

2 cos^{2} (w) - cos (w) - 1 = 0

What is the general solution for cos(3x)=-sin(x+pi/6) ?
The general solution for cos(3x)=-sin(x+pi/6) is x=(pi(3n+1))/3 ,x=-(pi(3n+1))/6