Question

(sin^2 a + sin a * cos a)/(cos^2 a + sin a * cos a)

Answer 1

Ответ: tga.

Упростите триг. выражение.

Answer 2

To simplify the given expression, we can use trigonometric identities. Let's work on it step by step:

Expression: (sin^2 a + sin a * cos a) / (cos^2 a + sin a * cos a)

First, notice that both the numerator and denominator have a common factor of sin(a) * cos(a). Let's factor it out:

(sin a * cos a) * (sin a + 1) / (sin a * cos a + cos^2 a)

Now, we can cancel out the common factor of sin(a) * cos(a) from both the numerator and denominator:

(sin a + 1) / (cos a + cos^2 a / sin a)

Next, we can use the Pythagorean identity for sine and cosine:

sin^2 a + cos^2 a = 1

So, rearranging the above equation, we have:

cos^2 a = 1 - sin^2 a

Now, substitute this into the denominator:

(sin a + 1) / (cos a + 1 - sin^2 a / sin a)

Now, distribute sin(a) in the denominator:

(sin a + 1) / (cos a + (sin a - sin^2 a) / sin a)

Combine the terms in the denominator:

(sin a + 1) / (cos a + sin a - sin a)

Notice that the terms "sin a" in the denominator cancel out:

(sin a + 1) / cos a

So, the simplified expression is:

(sin a + 1) / cos a

This is the simplified form of the given expression.