What is the general solution for sin(5x)+sin(7x)=0,-90<= x<90 ?

The general solution for sin(5x)+sin(7x)=0,-90<= x<90 is x=-90,x=0,x=30,x=60,x=-60,x=-30

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sin(5x)+sin(7x)=0,-90<= x<90

sin (5 x) + sin (7 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

x = - 9 0^{\circ}, x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}

Solution steps

sin (5 x) + sin (7 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ}

Rewrite using trig identities

2 cos (x) sin (6 x) = 0

Solving each part separately

cos (x) = 0 or sin (6 x) = 0

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

sin (6 x) = 0, - 9 0^{\circ} \leq x < 9 0^{\circ} : x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}, x = - 9 0^{\circ}

Combine all the solutions

x = - 9 0^{\circ}, x = 0, x = 3 0^{\circ}, x = 6 0^{\circ}, x = - 6 0^{\circ}, x = - 3 0^{\circ}

- cos (θ) + 1 = 2 sin^{2} (θ)

arcsin (x) = \frac{3 π}{7}

tan (a) = \frac{3}{4}

3 tan (x) + 3 = 0

cos (π x) = 0.5

What is the general solution for sin(5x)+sin(7x)=0,-90<= x<90 ?
The general solution for sin(5x)+sin(7x)=0,-90<= x<90 is x=-90,x=0,x=30,x=60,x=-60,x=-30