Question

4 sin x cos x cos 2 x=

Answer 1

Ответ:

4sin*(2x)*cos(2x);

sin(4x)

Ответ: sin(4x)

Объяснение:

Answer 2

Let's simplify the expression step by step. We'll use trigonometric identities to simplify the given expression:

1. Use the double angle identity: cos(2x) = 2cos^2(x) - 1.
2. Rewrite sin(x)cos(x) as 0.5sin(2x).

Now, let's substitute these simplifications back into the original expression:

4 * (0.5sin(2x)) * (2cos^2(x) - 1)

Simplify further:

2sin(2x) * (2cos^2(x) - 1)

Now, we can use the double angle identity for sine: sin(2x) = 2sin(x)cos(x).

Substitute this into the expression:

2 * 2sin(x)cos(x) * (2cos^2(x) - 1)

Now, expand the expression:

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

Simplify:

4sin(x)cos(x) * (4cos^2(x) - 1) = 16sin(x)cos^3(x) - 4sin(x)cos(x)

So, 4sin(x)cos(x)cos(2x) simplifies to 16sin(x)cos^3(x) - 4sin(x)cos(x) using trigonometric identities.