Find the solutions/ show steps
Sin2x+sin(4x) =0

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

Step-by-step explanation:

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

Use double angle formula.

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

Factor.

sin(2x) (1 + 2 cos(2x)) = 0

Solve.

sin(2x) = 0, cos(2x) = -½

2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3

x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3

each side has a different length.  

step-by-step explanation:

wholesale price is the initial price before markup. retail price comes after the markup.

a price of 8 bucks that's marked up by 100%   is

formula: initial price + (percent markup in fraction/decimal)(initial price)

8+(1)(8)

8+8

16

retail price is $16.