894 Вправа 894Геометрія 8 клас Бурда 2025 · § 16 · стор. 180

894. Знайдіть значення виразу: 1) tg 30° · tg 60°; 2) ${\displaystyle \sqrt{\mathbf{2}}}$ cos 45° · tg 45°; 3) 2 sin 30° + ${\displaystyle \sqrt{\mathbf{3}}}$ cos 30°; 4) 6 cos 60° – ${\displaystyle \sqrt{\mathbf{3}}}$ tg 30°.

1) tg 30° · tg 60° = ${\displaystyle \frac{\sqrt{\mathbf{3}}}{\mathbf{3}}}$ · ${\displaystyle \sqrt{\mathbf{3}}}$ = ${\displaystyle \frac{\mathbf{3}}{\mathbf{3}}}$ = 1;

2) ${\displaystyle \sqrt{\mathbf{2}}}$ cos 45° · tg 45° = ${\displaystyle \sqrt{\mathbf{2}}}$ · ${\displaystyle \frac{\sqrt{\mathbf{2}}}{\mathbf{2}}}$ · 1 = ${\displaystyle \frac{\mathbf{2}}{\mathbf{2}}}$ = 1;

3) 2 sin 30° + ${\displaystyle \sqrt{\mathbf{3}}}$ cos 30° = 2 · ${\displaystyle \frac{\mathbf{1}}{\mathbf{2}}}$ + ${\displaystyle \sqrt{\mathbf{3}}}$ · ${\displaystyle \frac{\sqrt{\mathbf{3}}}{\mathbf{2}}}$ =

= 1 + ${\displaystyle \frac{\mathbf{3}}{\mathbf{2}}}$ = 1 + 1,5 = 2,5;

4) 6 cos 60° – ${\displaystyle \sqrt{\mathbf{3}}}$ tg 30° = 6 · ${\displaystyle \frac{\mathbf{1}}{\mathbf{2}}}$ – ${\displaystyle \sqrt{\mathbf{3}}}$ · ${\displaystyle \frac{\sqrt{\mathbf{3}}}{\mathbf{3}}}$ =

= 3 – ${\displaystyle \frac{\mathbf{3}}{\mathbf{3}}}$ = 3 – 1 = 2.

Відповідь: 1) 1; 2) 1; 3) 2,5; 4) 2.