Question

sin4x cosx-cos4x sinx >√2/2

Answer 1

Решение:
$sin4xcos x - cos4xsin x textgreater frac{sqrt2}{2} \ sin(4x-x) textgreater frac{sqrt2}{2} \ sin3x textgreater frac{sqrt2}{2} \ frac{3pi}{4}+pi k textgreater 3x textgreater frac{pi}{4} + pi k \ \ frac{pi}{4} + frac{pi k}{3} textgreater x textgreater frac{pi}{12} + frac{pi k}{3}$