Sin3(2x) = 1/2sin(2x) [1 − cos(4x)]

I suppose we start with sin³(2*x) and we want to get:

(1/2)*sin(2*x)*(1 - cos(4*x))

Here we will use the relationships:

cos²(x) + sin²(x) = 1

and

cos²(x) = (1 + cos(2x))/2

Now let's start:

sin³(2*x) = sin(2*x)*sin²(2*x)

and we can write:

sin²(2*x) = 1 - cos²(2*x)

replacing that in the above equation we get:

sin³(2*x) = sin(2*x)*sin²(2*x) = sin(2*x)*(1 - cos²(2*x))

now we can use: cos²(2*x) =  (1 + cos(2*2*x))/2

cos²(2*x) =  (1 + cos(4*x))/2

if we replace that in the equation above we get:

sin³(2*x) = sin(2*x)*(1 - cos²(2*x)) = sin(2*x)*( 1 -  (1 + cos(4*x))/2)

sin³(2*x) = sin(2*x)*( 1 -  1/2 - cos(4*x)/2)

sin³(2*x) = sin(2*x)*( 1/2 - cos(4*x)/2)

sin³(2*x) = sin(2*x)*(  1 - cos(4*x))/2

sin³(2*x) = (1/2)*sin(2*x)*(  1 - cos(4*x))

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

can you make your screen more see able?

then i might be able to .