What is the general solution for sin(4x)+sin(2x)=0,0<= x<= 180 ?

The general solution for sin(4x)+sin(2x)=0,0<= x<= 180 is x=90,x=0,x=60,x=120,x=180

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sin(4x)+sin(2x)=0,0<= x<= 180

sin (4 x) + sin (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

x = 9 0^{\circ}, x = 0, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 18 0^{\circ}

Solution steps

sin (4 x) + sin (2 x) = 0, 0^{\circ} \leq x \leq 18 0^{\circ}

Rewrite using trig identities

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

Solving each part separately

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

cos (x) = 0, 0 \leq x \leq 18 0^{\circ} : x = 9 0^{\circ}

sin (3 x) = 0, 0 \leq x \leq 18 0^{\circ} : x = 0, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 18 0^{\circ}

Combine all the solutions

x = 9 0^{\circ}, x = 0, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 18 0^{\circ}

\frac{3 tan ( x )}{sec ( x )} - cos (x) = 0

2 cos (2 x) = 2

sec^{2} (θ) - 2 tan (θ) = 0

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

5 tan^{2} (x) - tan (x) = 0

What is the general solution for sin(4x)+sin(2x)=0,0<= x<= 180 ?
The general solution for sin(4x)+sin(2x)=0,0<= x<= 180 is x=90,x=0,x=60,x=120,x=180