Question

1+2sinacosa/(sina+cosa)2=1​

Answer 1

Ответ:

решение на фотографии

Answer 2

To solve the equation $1 + 2\sin(a)\cos(a)/(\sin(a) + \cos(a))^2 = 1$, we'll start by simplifying the left-hand side and then finding the values of $a$ that satisfy the equation.

Let's simplify the left-hand side step by step:

1. Expand the denominator:

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

2. Substitute into the equation:

   $$\frac{2\sin(a)\cos(a)}{\sin^2(a) + 2\sin(a)\cos(a) + \cos^2(a)} = 0$$

3. Multiply both sides by the denominator:

   $$2\sin(a)\cos(a) = 0$$

Now, we have two possibilities for this equation to hold true:

• Case 1: $\sin(a) = 0$: This occurs when $a = k\pi$ where $k$ is an integer.

• Case 2: $\cos(a) = 0$: This occurs when $a = \frac{\pi}{2} + k\pi$ or $a = \frac{3\pi}{2} + k\pi$ where $k$ is an integer.

So, the general solutions for $a$ that satisfy the given equation are: $a = k\pi, \frac{\pi}{2} + k\pi, \frac{3\pi}{2} + k\pi$ where $k$ is an integer.