It looks like the given equation is
sin(2x) - sin(2x) cos(2x) = sin(4x)
Recall the double angle identity for sine:
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
sin(2x) - sin(2x) cos(2x) = 2 sin(2x) cos(2x)
Move everything over to one side and factorize:
sin(2x) - sin(2x) cos(2x) - 2 sin(2x) cos(2x) = 0
sin(2x) - 3 sin(2x) cos(2x) = 0
sin(2x) (1 - 3 cos(2x)) = 0
Then we have two families of solutions,
sin(2x) = 0 or 1 - 3 cos(2x) = 0
sin(2x) = 0 or cos(2x) = 1/3
[2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
(where n is any integer)
[2x = 2nπ or 2x = π + 2nπ]
… … … or [2x = arccos(1/3) + 2nπ or 2x = -arccos(1/3) + 2nπ]
[x = nπ or x = π/2 + nπ]
… … … or [x = 1/2 arccos(1/3) + nπ or x = -1/2 arccos(1/3) + nπ]
Answer:
Step-by-step explanation:
Alright, lets get started.
Tomas has four pieces of wood having each length = 5, 4, 6 and 3
The length of wood he needs to cut to make a model airplane = 
Simplifying, it is 3.32 feet long
Means he needs more than 3 feet but less than 4 feet of wood piece.
So, he should select 4 feet length of wood because selcting 3 feet will not fulfilled to make his model and selcting 5 and 6 feet will have more unused wood.
4 feet piece of wood he should cut to have the least amount of unused wood. : Answer
Hope it will help :)
Answer:
James was 35 feet from the ground
Step-by-step explanation:
17 - 7 + 25
10 + 25
= 35
Answer:
There are 220 students at Marie's school :)
