Question

Sina+sinb если a+b =3п; a-b=п/3a альфаb бета

Answer 1

Sina + sinb = 2 *sin(a + b)/2 * cos (a - b)/2 ==>

2 *sin (3pi/2) * cos (pi/3)/2 = 2*(-1)*√3/2 = - √3

Answer 2

It looks like the question involves solving a system of equations with the variables a and b, and the given equations are:

1. a + b = 3p 2. a - b = p/3

It also mentions the expressions 3a + αb + β, which seems to be related to the context of the problem.

To solve for the values of a and b, we can use the method of substitution or elimination. Let's start by solving this system of equations step by step.

Step 1: Solving for a and b

We can solve this system by adding the two equations to eliminate b:

a + b + a - b = 3p + p/3 2a = 3p + p/3 2a = (9p + p) / 3 2a = 10p / 3 a = 5p / 3

Substitute the value of a in one of the original equations to solve for b:

5p / 3 - b = 3p b = 5p / 3 - 3p b = 5p / 3 - 9p / 3 b = (5p - 9p) / 3 b = -4p / 3

So, the solutions for a and b are: a = 5p / 3 b = -4p / 3

Step 2: Expressions 3a + αb + β

The expressions 3a + αb + β can be evaluated using the values we found for a and b: 3a + αb + β = 3 * (5p / 3) + α * (-4p / 3) + β 3a + αb + β = 5p + (-4αp / 3) + β

This is the expression in terms of p, α, and β based on the values of a and b we found.

If there is additional context or specific values for α and β, please provide that information so I can help further with the evaluation of the expression.