What is the general solution for sin(2x)-4*cos(x)=0 ?

The general solution for sin(2x)-4*cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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sin(2x)-4*cos(x)=0

sin (2 x) - 4 \cdot cos (x) = 0

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

Solution steps

sin (2 x) - 4 cos (x) = 0

Rewrite using trig identities

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

Factor

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

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

Solving each part separately

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

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

sin (x) - 2 = 0 :

No Solution

Combine all the solutions

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

5 tan (θ) + 3 = 0

sin (θ) = - \frac{4}{7}, π < θ < \frac{3 π}{2}, cos (2 θ)

tan (θ) = - \frac{2}{5}

(tan (x) - 1) (3 tan (x) + 1) = 0

sec (2 x) + 1 = 0

What is the general solution for sin(2x)-4*cos(x)=0 ?
The general solution for sin(2x)-4*cos(x)=0 is x= pi/2+2pin,x=(3pi)/2+2pin