Question

Sin^2 (2pi + a) + cos^2 (6pi - a) + 1

Answer 1

Ответ:

Пошаговое объяснение:

Sin^2 (2pi + a) + cos^2 (6pi - a) + 1 = sin²α + cos²α +1 = 2

Answer 2

Let's simplify the expression step by step:

1. Recall that the trigonometric identity for sine and cosine is:

   $\sin^2(x) + \cos^2(x) = 1$

   This identity states that the sum of the squares of sine and cosine of the same angle $x$ is always equal to 1.

2. In the given expression, we have:

   $\sin^2(2\pi + a) + \cos^2(6\pi - a) + 1$

   Let's focus on the first two terms:

   $\sin^2(2\pi + a)$ and $\cos^2(6\pi - a)$

3. For any angle $x$, the sine and cosine functions are periodic with a period of $2\pi$. This means that:

   $\sin(2\pi + x) = \sin(x)$ $\cos(2\pi + x) = \cos(x)$

   Therefore, in our expression, we can simplify as follows:

   $\sin^2(2\pi + a) = \sin^2(a)$ $\cos^2(6\pi - a) = \cos^2(-a) = \cos^2(a)$

4. Now, we have:

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

5. Using the trigonometric identity mentioned in step 1, we can simplify further:

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

6. Finally, we add 1 to the result:

   $1 + 1 = 2$

So, the simplified expression is $2$.