Question

Sin8п/7cos п/7-cos8п/7sinп/7

Answer 1

Sin8π/7cosπ/7-cos8π/7sinπ/7=sin(8π/7-π/7)=sinπ=0

Answer 2

It seems like you've provided a trigonometric expression involving angles in radians. Let's break down the expression step by step:

The given expression is: $\sin\left(\frac{8\pi}{7}\right)\cos\left(\frac{\pi}{7}\right) - \cos\left(\frac{8\pi}{7}\right)\sin\left(\frac{\pi}{7}\right)$

We can use the angle sum formula for sine and cosine to simplify this expression. The angle sum formula for sine is $\sin(A - B) = \sin A \cos B - \cos A \sin B$. Similarly, the angle sum formula for cosine is $\cos(A - B) = \cos A \cos B + \sin A \sin B$.

Let's compare the given expression with the angle sum formulas:

$A = \frac{8\pi}{7}$ and $B = \frac{\pi}{7}$

Using the angle sum formulas for sine and cosine:

$\sin\left(\frac{8\pi}{7} - \frac{\pi}{7}\right) = \sin\left(\frac{7\pi}{7}\right) = \sin(\pi) = 0$ $\cos\left(\frac{8\pi}{7} - \frac{\pi}{7}\right) = \cos\left(\frac{7\pi}{7}\right) = \cos(\pi) = -1$

So, the simplified expression is $0 - (-1)$, which simplifies to $1$.

Therefore, the value of the given expression is $1$.