Hi there!
We are given:
cos(7x)cos(4x) = -1 - sin(7x)sin(4x)
Begin by moving all terms with variables to one side:
cos(7x)cos(4x) + sin(7x)sin(4x) = -1
The corresponding trig identity is cos(A - B). Thus:
cos(7x - 4x) = cos(7x)cos(4x) + sin(7x)sin(4x) = -1
cos(3x) = -1
cos = -1 at π, so:
3x = π
x = π/3
We can also find another solution. Let 3π = -1:
3x = 3π
x = π
Thus, solutions on [0, 2π) are π/3 and π.
Answer:
The numbers are 9, 19 and 76.
Step-by-step explanation:
Let's take the second number and make it a variable, like x. Now let's find all the other numbers in terms of x.
The first number in terms of x:
The second number in terms of x:
If we add them all up, these 3 numbers in terms of x must be equal to 104, so:
Now that we know the second number, we can find the other numbers since we already figured out their values in terms of x:
The first number is 9, second number 19 and the third number 76.