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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.
<h2>Greetings!</h2>
<h2>Hope this helps!</h2>
Answer:
t =
Step-by-step explanation:
First, you need to complete the -3 + 1 and then expand the brackets
-3 + 1 = -2
7t -2 - (-2) = -3(1 - 3t)
Now expant the -3(1 - 3t) bracket
-3 * 1 = -3
-3 * -3t = 9t
7t - 2 - -2 = 9t - 3
The two negatives turn positive:
7t - 2 + 2 = 9t - 3
7t = 9t - 3
Move the -3 over to the oposite side, and also move the +7t over to the +9t, making it a negative:
3 = 9t - 7t
3 = 2t
Divide both sides by 2:
t =
So the value of t is
<h2>Hope this helps!</h2>