Question

(Cos a /1+sin a + cos a/ 1-sin a ) * sin 2 a

Answer 1

Можно много заниматься ,

Answer 2

To simplify the expression $\frac{\cos(a)}{1+\sin(a)} + \frac{\cos(a)}{1-\sin(a)}$ multiplied by $\sin(2a)$, we can follow these steps:

Step 1: Find a common denominator for the two fractions on the left side of the expression.

$\frac{\cos(a)}{1+\sin(a)} + \frac{\cos(a)}{1-\sin(a)} = \frac{\cos(a)(1-\sin(a))}{(1+\sin(a))(1-\sin(a))} + \frac{\cos(a)(1+\sin(a))}{(1-\sin(a))(1+\sin(a))}$

Step 2: Simplify the fractions by multiplying the numerators and denominators.

$\frac{\cos(a)(1-\sin(a))}{(1+\sin(a))(1-\sin(a))} + \frac{\cos(a)(1+\sin(a))}{(1-\sin(a))(1+\sin(a))} = \frac{\cos(a)(1-\sin(a)) + \cos(a)(1+\sin(a))}{(1-\sin(a))(1+\sin(a))}$

Step 3: Combine the terms in the numerator.

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

Step 4: Simplify the denominator.

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

Step 5: Rewrite $\sin^2(a)$ as $\cos^2(a)$ using the trigonometric identity $\sin^2(a) + \cos^2(a) = 1$.

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

Now, we have:

$\frac{2\cos(a)}{\cos^2(a)}$

Step 6: Cancel out a factor of $\cos(a)$ in the numerator and denominator.

$\frac{2\cancel{\cos(a)}}{\cancel{\cos(a)}\cos(a)} = \frac{2}{\cos(a)}$

Step 7: Multiply the result by $\sin(2a)$.

$\frac{2}{\cos(a)} \cdot \sin(2a) = 2\sin(2a)$

So, the simplified expression is $2\sin(2a)$.