Question

Please help me with this question!! I also need the steps

Answer 1

Hi there!

$\large\boxed{x = \frac{\pi}{3} \text{ and } \pi}$

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.