Question

Sina cosB-sin(a-B)​cos a cos B - cos(a-B)1-tgx / 1+tgx

Answer 1

Объяснение:

$sin \alpha cos \beta - sin( \alpha - \beta ) = sin \alpha cos \beta - sin \alpha cos \beta + cos \alpha sin \beta = cos \alpha sin \beta .$

$os \alpha cos \beta - cos( \alpha - \beta ) = cos \alpha cos \beta - cos \alpha os \beta - sin \alpha sin \beta = - sin \alpha sin \beta$

$\frac{1 - tgx}{1 + tgx} = \frac{1 - \frac{sinx}{cosx} }{1 + \frac{sinx}{cosx} } = \frac{cosx - sinx}{cosx + sinx} = \frac{sin( \frac{\pi}{2} - x) - sinx}{sin( \frac{\pi}{2} - x) + sinx } = \frac{2sin( \frac{\pi}{4} - x)cos \frac{\pi}{4} }{2sin \frac{\pi}{4}cos( \frac{\pi}{4} - x) } = tg( \frac{\pi}{4} - x)$

Answer 2

It seems like you've provided a mathematical expression involving trigonometric functions and an algebraic expression. Let's break it down and simplify it step by step.

The expression you've given is: $\sin(a) \cos(B) - \sin(a - B) \cos(a) \cos(B) - \frac{\cos(a - B)(1 - \tan(x))}{1 + \tan(x)}$

Let's simplify this step by step using trigonometric identities:

1. Trigonometric Identities:

   • $\tan(x) = \frac{\sin(x)}{\cos(x)}$
   • $\sin(a - B) = \sin(a)\cos(B) - \cos(a)\sin(B)$

2. Substitute $\sin(a - B)$ using the identity: $\sin(a) \cos(B) - (\sin(a)\cos(B) - \cos(a)\sin(B)) \cos(a) \cos(B) - \frac{\cos(a - B)(1 - \tan(x))}{1 + \tan(x)}$

3. Simplify further: $\sin(a) \cos(B) - \sin(a)\cos(B)\cos(a)\cos(B) + \cos(a)\sin(B)\cos(a)\cos(B) - \frac{\cos(a)\cos(B)(1 - \tan(x))}{1 + \tan(x)}$

4. Use $\tan(x) = \frac{\sin(x)}{\cos(x)}$: $\sin(a) \cos(B) - \sin(a)\cos(B)\cos(a)\cos(B) + \cos(a)\sin(B)\cos(a)\cos(B) - \frac{\cos(a)\cos(B)(1 - \frac{\sin(x)}{\cos(x)})}{1 + \frac{\sin(x)}{\cos(x)}}$

5. Further Simplify: $\sin(a) \cos(B) - \sin(a)\cos(B)\cos(a)\cos(B) + \cos(a)\sin(B)\cos(a)\cos(B) - \frac{\cos(a)\cos(B)\cos(x) - \cos(a)\cos(B)\sin(x)}{\cos(x) + \sin(x)}$

6. Combine Terms: $\sin(a) \cos(B) - \frac{\sin(a)\cos(B)\cos(a)\cos(B) - \cos(a)\cos(B)\cos(x) + \cos(a)\cos(B)\sin(x)}{\cos(x) + \sin(x)}$

Please note that this expression may be further simplified or manipulated depending on specific conditions or relationships between $a$, $B$, and $x$. If you have specific values or conditions, feel free to provide them, and I can help simplify the expression further.