What is the general solution for 3sin(2x)=3cos(x) ?

The general solution for 3sin(2x)=3cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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3sin(2x)=3cos(x)

3 sin (2 x) = 3 cos (x)

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

3 sin (2 x) = 3 cos (x)

Subtract

3 cos (x)

from both sides

3 sin (2 x) - 3 cos (x) = 0

Rewrite using trig identities

- 3 cos (x) + 6 cos (x) sin (x) = 0

Factor

- 3 cos (x) + 6 cos (x) sin (x) : 3 cos (x) (2 sin (x) - 1)

3 cos (x) (2 sin (x) - 1) = 0

Solving each part separately

cos (x) = 0 or 2 sin (x) - 1 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

4 sec (x) + 8 = 0

x, ln (y) = e^{y} sin (x)

2 sin^{2} (x) = 1 - sin (x)

tan (x) sin (2 x) = 0

5 sin (2 θ) = 7 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

What is the general solution for 3sin(2x)=3cos(x) ?
The general solution for 3sin(2x)=3cos(x) is x= pi/2+2pin,x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin