Now we see that the inequality simplifies to sin(x)cos(x)cos(2x) < 0.25.
To find the solutions for this inequality, we can use the unit circle and consider the signs of sin(x), cos(x), and cos(2x) in each quadrant. This will help us determine the intervals where the inequality holds true.
Alternatively, we can use trigonometric identities to simplify the expression further and solve for x.
To solve the inequality sin(2x) * cos(2x) < 0.25, we can start by using the double angle formulas for sine and cosine:
sin(2x) = 2sin(x)cos(x
cos(2x) = cos^2(x) - sin^2(x)
Substitute these formulas into the inequality:
2sin(x)cos(x) * (cos^2(x) - sin^2(x)) < 0.25
Expand and simplify:
2sin(x)cos(x)cos^2(x) - 2sin(x)cos(x)sin^2(x) < 0.25
sin(x)cos(x)(2cos^2(x) - 2sin^2(x)) < 0.25
sin(x)cos(x)(cos(2x)) < 0.25
Now we see that the inequality simplifies to sin(x)cos(x)cos(2x) < 0.25.
To find the solutions for this inequality, we can use the unit circle and consider the signs of sin(x), cos(x), and cos(2x) in each quadrant. This will help us determine the intervals where the inequality holds true.
Alternatively, we can use trigonometric identities to simplify the expression further and solve for x.