Question

Sin(a/2)*cos(a/2)*cosa

Answer 1

Решение задания прилагаю

Answer 2

The expression you've provided is a trigonometric expression involving the sine and cosine functions. Let's break it down step by step:

sin(a/2) * cos(a/2) * cos(a)

1. sin(a/2): This represents the sine of half of the angle 'a.'
2. cos(a/2): This represents the cosine of half of the angle 'a.'
3. cos(a): This represents the cosine of the angle 'a' itself.

To simplify this expression, you can use trigonometric identities. One useful identity is the double angle identity:

sin(2θ) = 2sin(θ)cos(θ)

Now, let's apply this identity to the expression:

sin(a/2) * cos(a/2) * cos(a)

Using the double angle identity, we can rewrite sin(a/2) * cos(a/2) as sin(a):

sin(a) * cos(a)

Now, you can use another trigonometric identity, the double angle identity for cosine:

cos(2θ) = cos^2(θ) - sin^2(θ)

Here, θ is equal to 'a.' So, let's substitute 'a' for θ:

cos(2a) = cos^2(a) - sin^2(a)

Now, we have:

sin(a) * (cos^2(a) - sin^2(a))

You can further simplify this expression if needed, but this is the result of the given expression in terms of trigonometric functions.