Question

Sin(п/4-a)sin(п/4+а)-cos(п/4+а)cos(п/4-а)

Answer 1

Ответ:

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Объяснение:

Answer 2

The expression you've provided seems to involve trigonometric functions. Let's simplify it step by step:

The expression is: $\sin\left(\frac{\pi}{4} - a\right) \sin\left(\frac{\pi}{4} + a\right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

We can start by using trigonometric identities to simplify this expression. One useful identity is the product-to-sum identity for sine: $\sin(A) \sin(B) = \frac{1}{2} \left( \cos(A - B) - \cos(A + B) \right)$

Using this identity, we can rewrite the expression: $\frac{1}{2} \left( \cos\left(\frac{\pi}{4} - a - \frac{\pi}{4} - a\right) - \cos\left(\frac{\pi}{4} - a + \frac{\pi}{4} + a\right) \right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

Simplifying further: $\frac{1}{2} \left( \cos\left(-\frac{\pi}{2} - 2a\right) - \cos\left(\frac{\pi}{2}\right) \right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

Since $\cos\left(\frac{\pi}{2}\right) = 0$, we have: $\frac{1}{2} \left( -\cos\left(\frac{\pi}{2} + 2a\right) \right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

Another trigonometric identity we can use is the cosine of a sum identity: $\cos(A - B) = \cos(A) \cos(B) + \sin(A) \sin(B)$

Applying this identity: $-\frac{1}{2} \cos\left(\frac{\pi}{2} + 2a\right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

Now, let's use the fact that $\cos\left(\frac{\pi}{2} + x\right) = -\sin(x)$: $-\frac{1}{2} \left( -\sin(2a) \right) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

Simplifying further: $\frac{1}{2} \sin(2a) - \cos\left(\frac{\pi}{4} + a\right) \cos\left(\frac{\pi}{4} - a\right)$

At this point, you might be able to apply the difference of cosine formula to simplify it even further: $\cos(A) \cos(B) = \frac{1}{2} \left( \cos(A + B) + \cos(A - B) \right)$