Question

(cos альфа + 1) (cos альфа -1)

Answer 1

Решение задания смотри на фотографии

Answer 2

To simplify the expression $(\cos \alpha + 1)(\cos \alpha - 1)$, we can use the difference of squares identity, which states that $a^2 - b^2 = (a + b)(a - b)$. In this case, we can treat $\cos \alpha$ as $a$ and 1 as $b$. So, the expression becomes:

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

Now, recall the trigonometric identity $\cos^2 \theta + \sin^2 \theta = 1$. By rearranging this identity, we get $\cos^2 \theta = 1 - \sin^2 \theta$.

Substituting $\theta = \alpha$, we have:

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

Substitute this back into the original expression:

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

So, the simplified expression is $-(\sin \alpha)^2$.