What is the general solution for -sin(2x)-3cos(x)=0 ?

The general solution for -sin(2x)-3cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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

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

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

Solution steps

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

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

cos (x) = 0 or 2 sin (x) + 3 = 0

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

2 sin (x) + 3 = 0 :

No Solution

Combine all the solutions

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

x, y = 3 cos (f xx + \frac{π}{2}) + 5

sin (x) cos (x) = sin (x), 0 < x \leq 2 π

cos^{5} (x) - sin (x) = 0

x, y = \frac{1}{5 sin ( 2 x )}

cos (θ) = \frac{3}{35}

What is the general solution for -sin(2x)-3cos(x)=0 ?
The general solution for -sin(2x)-3cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin