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.
<u>Given</u>:
Let A denote the angle of the given triangle which measures ∠A = 81°
Let B denote the angle which measures ∠B = 40°
The length of the side a = x.
The length of the side b = 7 cm.
We need to determine the value of x.
<u>Value of x:</u>
The value of x can be determined using the law of sine formula.
Applying the law of sine, we have;
Substituting the values, we have;
Simplifying, we get;
Cross multiplying, we have;
Thus, the length of the side x is 10.8 cm.
