Question

1-cos2a______=sin(П-а)

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

To simplify the expression $1 - \cos(2a)$, we can use the double angle formula for cosine, which states that $\cos(2a) = 2\cos^2(a) - 1$. So, $1 - \cos(2a)$ would be:

$1 - (2\cos^2(a) - 1) = 1 - 2\cos^2(a) + 1 = 2 - 2\cos^2(a) = 2(1 - \cos^2(a)).$

Now, we can use the trigonometric identity $\sin^2(x) + \cos^2(x) = 1$ to rewrite $2(1 - \cos^2(a))$ as $2\sin^2(a)$. Therefore, we have:

$1 - \cos(2a) = 2\sin^2(a).$

Next, we'll work on the right-hand side of the equation. Using the angle difference formula for sine, we have:

$\sin(\pi - a) = \sin(\pi)\cos(a) - \cos(\pi)\sin(a).$

Since $\sin(\pi) = 0$ and $\cos(\pi) = -1$, we get:

$\sin(\pi - a) = 0 - (-\sin(a)) = \sin(a).$

Now, we have:

$1 - \cos(2a) = 2\sin^2(a) = \sin(a).$

Therefore, the equation $1 - \cos(2a) = \sin(\pi - a)$ is indeed true.