Question

Sina +sin 3a+sin 5a +sin 7a =4 a cos cos 2a sin 4a

Answer 1

ответ:

sin6

cos3

A9 думаю что так

Answer 2

The equation you've provided seems to involve trigonometric functions and identities. Let's work through it step by step to verify the given equation:

Left-hand side (LHS): Sina + sin 3a + sin 5a + sin 7a

Right-hand side (RHS): 4a cos cos 2a sin 4a

Let's first apply some trigonometric identities:

1. sin(3a) = 3sin(a) - 4sin^3(a)
2. sin(5a) = 5sin(a) - 20sin^3(a) + 16sin^5(a)
3. sin(7a) = 7sin(a) - 56sin^3(a) + 112sin^5(a) - 64sin^7(a)
4. cos(2a) = 1 - 2sin^2(a)
5. sin(4a) = 4sin(a) - 8sin^3(a) + 4sin^5(a)

Now we can substitute these identities into the equation:

LHS = sin(a) + (3sin(a) - 4sin^3(a)) + (5sin(a) - 20sin^3(a) + 16sin^5(a)) + (7sin(a) - 56sin^3(a) + 112sin^5(a) - 64sin^7(a))

RHS = 4a * (1 - 2sin^2(a)) * (4sin(a) - 8sin^3(a) + 4sin^5(a))

Let's simplify both sides of the equation step by step:

LHS = sin(a) + 3sin(a) - 4sin^3(a) + 5sin(a) - 20sin^3(a) + 16sin^5(a) + 7sin(a) - 56sin^3(a) + 112sin^5(a) - 64sin^7(a) = 16sin(a) - 80sin^3(a) + 128sin^5(a) - 64sin^7(a)

RHS = 4a * (4sin(a) - 8sin^3(a) + 4sin^5(a) - 8sin^3(a) + 16sin^5(a) - 8sin^7(a)) = 16asin(a) - 64asin^3(a) + 64asin^5(a) - 32asin^7(a)

Now, it's clear that the LHS and RHS are not equal. The equation you've provided, "Sina + sin 3a + sin 5a + sin 7a = 4a cos cos 2a sin 4a," is not true as it stands. There might be a mistake in the equation or some missing context. If you can provide more information or clarify any discrepancies, I'd be happy to help further.