Question

2 cos (a+b) cos (a-b) - cos 2b​

Answer 1

Ответ:

$\cos (2 a)$

Объяснение:

Answer 2

To simplify the given expression, we can use trigonometric identities. Here's the step-by-step simplification:

1. Use the double-angle formula for cosine: cos(2x) = 2 * cos^2(x) - 1

2. Apply the double-angle formula to the last term (cos^2(b)): cos^2(b) = (1 + cos(2b)) / 2

Now, let's proceed with the simplification:

2 cos(a + b) cos(a - b) - cos(2b)

Step 1: Expand the product of cosines using the sum-to-product identity: cos(a + b) cos(a - b) = (1/2) * [cos(2a) + cos(2b)]

Step 2: Substitute the expression for cos(2b) using the double-angle formula: cos(2b) = 2 * cos^2(b) - 1 cos(2b) = 2 * [(1 + cos(2b)) / 2] - 1 cos(2b) = 1 + cos(2b) - 1 cos(2b) = cos(2b)

Step 3: Replace cos(2b) with cos(2b) in the expression: 2 cos(a + b) cos(a - b) - cos(2b) = 2 * [(1/2) * (cos(2a) + cos(2b))] - cos(2b) = cos(2a) + cos(2b) - cos(2b)

Step 4: Cancel out the common term cos(2b): = cos(2a)

So, the simplified expression is cos(2a).