Question

1)sina + sin 3a + sin 5acosa + cos 3a + cos 5a​

Answer 1

Смотри.............................

Answer 2

To simplify the given expression, we can start by using the trigonometric identity:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

Let's apply this identity to the expression:

sin(a) + sin(3a) + sin(5a)cos(a) + cos(3a) + cos(5a)

Rearranging the terms:

sin(a) + sin(3a) + cos(3a) + sin(5a)cos(a) + cos(5a)

Now, let's further simplify the expression:

Group the sine terms and cosine terms separately:

(sin(a) + cos(3a) + cos(5a)) + (sin(3a) + sin(5a)cos(a))

Notice that the term sin(5a)cos(a) can be rewritten using the following identity:

sin(2θ) = 2sin(θ)cos(θ)

sin(5a)cos(a) = sin(2a + 3a) = 2sin(2a)cos(3a)

Now, we can rewrite the expression:

(sin(a) + cos(3a) + cos(5a)) + (sin(3a) + 2sin(2a)cos(3a))

And that is the simplified form of the given expression.