Решите неравенство: sin x × cos pi÷10 - cos x × sin pi÷10 ≥ √2÷2;

Question

Решите неравенство: sin x × cos pi÷10 - cos x × sin pi÷10 ≥ √2÷2;

Answer 1

Sin x•cos π/10 - cos x•sin π/10 >= sqrt2/2
sin (x - π/10) >= sqrt2/2
π/4 + 2πn <= x - π/10 <= 3π/4 + 2πn, n є Z<br>π/4 + π/10 + 2πn <= x <= 3π/4 + π/10 + 2πn, n є Z<br>7π/20 + 2πn <= x <= 17π/20 + 2πn, n є Z<br>x є [7π/20 + 2πn; 17π/20 + 2πn], n є Z