Question

Sin 2a/ cos^2 a - sin^2a​

Answer 1

Ответ:

Объяснение:

= sin2a /cos2a=tg2a

Answer 2

To simplify the expression $\frac{\sin(2a)}{\cos^2(a) - \sin^2(a)}$, we can use trigonometric identities to rewrite it in a more manageable form.

First, we can use the double-angle identity for sine:

$\sin(2a) = 2\sin(a)\cos(a)$

Now, let's rewrite the denominator using the Pythagorean identity:

$\cos^2(a) - \sin^2(a) = \cos^2(a) - (1 - \cos^2(a))$ (using $\sin^2(a) = 1 - \cos^2(a)$)

Now, we have:

$\cos^2(a) - (1 - \cos^2(a)) = \cos^2(a) - 1 + \cos^2(a)$

Simplify the denominator:

$2\cos^2(a) - 1$

Now, our expression becomes:

$\frac{2\sin(a)\cos(a)}{2\cos^2(a) - 1}$

Now, you can see that both the numerator and denominator have a common factor of 2. We can cancel this common factor:

$\frac{\sin(a)\cos(a)}{\cos^2(a) - \frac{1}{2}}$

So, the simplified expression is:

$\frac{\sin(a)\cos(a)}{\cos^2(a) - \frac{1}{2}}$