Question

Sin(3п+а)+cos(п-а)-sin(-a)+cos(-a)

Answer 1

Ответ.................

Answer 2

To simplify the given expression, let's break it down step by step:

1. Sin(3π + α): Since the sine function has a period of 2π, we can add or subtract any multiple of 2π without changing the value. So, 3π is equivalent to π, and we have Sin(π + α).

2. Cos(π - α): Similar to the sine function, the cosine function also has a period of 2π. Therefore, π - α is equivalent to -α. So, we have Cos(-α).

3. Sin(-α): The sine function is an odd function, which means Sin(-x) = -Sin(x). Therefore, Sin(-α) = -Sin(α).

4. Cos(-α): The cosine function is an even function, which means Cos(-x) = Cos(x). So, Cos(-α) = Cos(α).

Now, let's substitute these simplified expressions back into the original equation:

Sin(3π + α) + Cos(π - α) - Sin(-α) + Cos(-α)

= Sin(π + α) + Cos(-α) - (-Sin(α)) + Cos(α)

= Sin(π + α) + Cos(α) + Sin(α) + Cos(α)

Now, we can see that we have two pairs of sin and cos terms. We can combine them:

= Sin(π + α) + 2Cos(α) + 2Sin(α)

So, the simplified form of the expression Sin(3π + α) + Cos(π - α) - Sin(-α) + Cos(-α) is Sin(π + α) + 2Cos(α) + 2Sin(α).