437 Найти значение выражения: 1) 2 sin x + √2 cos a при а = "; 4 2) 0,5 cos a √3 sin a при а α = 60°; 3) sin 3a cos 2a при а = 1; - a 4) cos+sin при а = . 2 3

1) 2 sin α + √2 cos α при α = $$ \frac{\pi}{4} $$

sin $$ \frac{\pi}{4} $$ = $$ \frac{\sqrt{2}}{2} $$. cos $$ \frac{\pi}{4} $$ = $$ \frac{\sqrt{2}}{2} $$.

2 × $$ \frac{\sqrt{2}}{2} $$ + √2 × $$ \frac{\sqrt{2}}{2} $$ = √2 + 1 = √2 + 1

Ответ: √2 + 1

2) 0,5 cos α - √3 sin α при α = 60°

cos 60° = $$ \frac{1}{2} $$. sin 60° = $$ \frac{\sqrt{3}}{2} $$

0, 5 × $$ \frac{1}{2} $$ - √3 × $$ \frac{\sqrt{3}}{2} $$ = $$ \frac{1}{4} $$ - $$ \frac{3}{2} $$ = $$ \frac{1}{4} $$ - $$ \frac{6}{4} $$ = - $$ \frac{5}{4} $$ = -1,25

Ответ: -1,25

3) sin 3α - cos 2α при α = $$ \frac{\pi}{6} $$

sin (3 × $$ \frac{\pi}{6} $$) - cos (2 × $$ \frac{\pi}{6} $$) = sin $$ \frac{\pi}{2} $$ - cos $$ \frac{\pi}{3} $$ = 1 - $$ \frac{1}{2} $$ = $$ \frac{1}{2} $$

Ответ: $$ \frac{1}{2} $$

4) cos $$ \frac{α}{2} $$ + sin $$ \frac{α}{3} $$ при α = $$ \frac{\pi}{2} $$

cos ($$ \frac{1}{2} $$ × $$ \frac{\pi}{2} $$) + sin ($$ \frac{1}{3} $$ × $$ \frac{\pi}{2} $$) = cos $$ \frac{\pi}{4} $$ + sin $$ \frac{\pi}{6} $$ = $$ \frac{\sqrt{2}}{2} $$ + $$ \frac{1}{2} $$ = $$ \frac{\sqrt{2} + 1}{2} $$

Ответ: $$ \frac{\sqrt{2} + 1}{2} $$