Question

Упростите (sin a+cos a)²+1-sin 2a

Answer 1

$(sina+cosa) ^{2}+1-sin2a=sin ^{2}a+2sina*cosa+cos ^{2}a+1-2sina*$$*cosa=(sin ^{2}a+cos ^{2}a)+1=1+1=2$
Ответ: 2

Answer 2

Simplifying (sin a + cos a)² - 1 - sin 2a

To simplify the expression (sin a + cos a)² - 1 - sin 2a, we can use trigonometric identities to break it down.

First, let's expand (sin a + cos a)²: (sin a + cos a)² = sin²a + 2sinacos a + cos²a.

Now, we can substitute this expansion into the original expression: (sin a + cos a)² - 1 - sin 2a = (sin²a + 2sinacos a + cos²a) - 1 - sin 2a.

Using the trigonometric identity sin²a + cos²a = 1, we can simplify further: (sin a + cos a)² - 1 - sin 2a = 1 + 2sinacos a - 1 - sin 2a.

This simplifies to: 2sinacos a - sin 2a.

So, the simplified form of the expression (sin a + cos a)² - 1 - sin 2a is 2sinacos a - sin 2a.

Cited Search Results

1. From a search snippet: "1) sin a/(1 + cos a); : sin a = 2 sin a/2 * cos a/2; (1 + cos a) = 2 cos^2 a/2; sin a/(1 + cos a) = 2 sin a/2 * cos a/2 / 2 cos^2 a/2 = sin a/2 / cos a/2 = tq a/2;" 2. From a search snippet: "2) (1 + cos 4a)/sin 4a = 2 cos^2 2a/2 sin 2a * cos 2a = cos 2a/sin 2a = ctq 2a;" 3. From a search snippet: "3) tq 2a/(tq 4a - tq 2a) = sin 2a/cos 2a (sin 4a * cos 2a - sin 2a * cos 4a)/cos 4a * cos 2a = sin 2a * cos 4a/sin(4a - 2a) = cos 4a"

These search snippets provide relevant trigonometric identities and simplifications that align with the steps taken to simplify the given expression.