Question

Cos(п/4-b)* cos(п/4+b)

Answer 1

Ответ:

Объяснение:

Cosа×Cosb=1/2[cos(a+b)+cos(a-b)]

Answer 2

The expression you've provided seems to be a product of two trigonometric functions:

$\cos\left(\frac{\pi}{4} - b\right) \cdot \cos\left(\frac{\pi}{4} + b\right)$

Here, $b$ is a constant angle in radians. To simplify this expression, you can use the trigonometric identity for the product of cosines:

$\cos(A) \cdot \cos(B) = \frac{1}{2} \left( \cos(A - B) + \cos(A + B) \right)$

Applying this identity to your expression:

\cos\left(\frac{\pi}{4} - b\right) \cdot \cos\left(\frac{\pi}{4} + b\right) &= \frac{1}{2} \left( \cos\left(\frac{\pi}{4} - b - \frac{\pi}{4} - b\right) + \cos\left(\frac{\pi}{4} - b + \frac{\pi}{4} + b\right) \right) \\ &= \frac{1}{2} \left( \cos\left(-2b\right) + \cos\left(\frac{\pi}{2}\right) \right) \\ &= \frac{1}{2} \left( \cos\left(-2b\right) + 0 \right) \\ &= \frac{1}{2} \cdot \cos\left(-2b\right) \\ &= \frac{1}{2} \cdot \cos\left(2b\right) \end{align*} \] So, the simplified expression for \( \cos\left(\frac{\pi}{4} - b\right) \cdot \cos\left(\frac{\pi}{4} + b\right) \) is \( \frac{1}{2} \cdot \cos(2b) \).