Question

Cos²a-cos(30°+a)cos(30°-a)​

Answer 1

Ответ:$cos(a)^{2} -\frac{cos(2a)}{2}-\frac{1}{4}$

Объяснение:

Answer 2

The expression you've provided, cos²a - cos(30°+a)cos(30°-a), can be simplified using trigonometric identities. Let's break down the steps:

1. Cosine Double Angle Formula: cos(2θ) = 2cos²θ - 1

Applying this formula, we can rewrite cos²a as (1 + cos(2a)) / 2:

cos²a = (1 + cos(2a)) / 2

2. Sum-to-Product Formula: cos(A + B)cos(A - B) = cos²A - cos²B

Applying this formula to the second term, where A = 30° and B = a:

cos(30° + a)cos(30° - a) = cos²30° - cos²a cos(30° + a)cos(30° - a) = (sqrt(3)/2)² - cos²a cos(30° + a)cos(30° - a) = 3/4 - cos²a

Now, substitute this result back into the original expression:

cos²a - cos(30° + a)cos(30° - a) = (1 + cos(2a)) / 2 - (3/4 - cos²a) cos²a - cos(30° + a)cos(30° - a) = 1/2 + cos²a - 3/4 cos²a - cos(30° + a)cos(30° - a) = 2cos²a - 1/4

So, the simplified expression is 2cos²a - 1/4.