Question

B) ctg^2a*sin^2a/1-sin^2a

Answer 1

Ответ:

все верно лайкни плз и дучши отв ctg2a×tg2a

Answer 2

To simplify the expression $\frac{\cot^2(a) \sin^2(a)}{1 - \sin^2(a)}$, you can start by using trigonometric identities to rewrite the terms in the expression:

1. Recall that $\cot(a) = \frac{1}{\tan(a)}$.
2. Also, $\tan^2(a) + 1 = \sec^2(a)$.

Now, let's rewrite the expression:

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

Now, you can use the identity $\sin^2(a) + \cos^2(a) = 1$ to simplify further:

$$\begin{align*} \frac{\frac{\sin^2(a)}{\cos^2(a)}}{1 - \sin^2(a)} &= \frac{\frac{\sin^2(a)}{\cos^2(a)}}{\cos^2(a)} \\ &= \frac{\sin^2(a)}{\cos^2(a) \cdot \cos^2(a)} \\ &= \frac{\sin^2(a)}{\cos^4(a)}. \end{align*}$$

So, the simplified expression is $\frac{\sin^2(a)}{\cos^4(a)}$.