Question

Sin a - cos a * (tg a + ctg a)

Answer 1

Ответ:

sin a - cos a( sin a/ cos a + cos a/ sin a)

sin a - sin a - cos² a/sin a=-cos² a/sin a

Answer 2

To simplify the expression $\sin(a) - \cos(a) \cdot (\tan(a) + \cot(a))$, you can start by simplifying the terms involving trigonometric functions:

1. Recall that $\cot(a)$ is the reciprocal of $\tan(a)$, so $\cot(a) = \frac{1}{\tan(a)}$.
2. Also, remember that $\tan(a) = \frac{\sin(a)}{\cos(a)}$.

Now, let's substitute these values into the expression:

$$\begin{align*} \sin(a) - \cos(a) \cdot \left(\tan(a) + \cot(a)\right) &= \sin(a) - \cos(a) \cdot \left(\frac{\sin(a)}{\cos(a)} + \frac{1}{\tan(a)}\right) \\ &= \sin(a) - \frac{\cos(a) \cdot \sin(a)}{\cos(a)} - \frac{\cos(a)}{\tan(a)} \\ &= \sin(a) - \sin(a) - \frac{\cos(a)}{\frac{\sin(a)}{\cos(a)}} \\ &= \sin(a) - \sin(a) - \frac{\cos^2(a)}{\sin(a)}. \end{align*}$$

Now, you can simplify further:

$$\begin{align*} \sin(a) - \sin(a) - \frac{\cos^2(a)}{\sin(a)} &= 0 - \frac{\cos^2(a)}{\sin(a)} \\ &= -\frac{\cos^2(a)}{\sin(a)}. \end{align*}$$

So, the simplified expression is $-\frac{\cos^2(a)}{\sin(a)}$.