Найдите значение выражений

A. sin15+cos15

B. cos75-sin75

Решение

A. sin15°+cos15° = √ (sin15+cos15) ² = √ (sin²15° + 2sin15°cos15° + cos²15°) =

= √[1 + sin (2*15°] = √ (1 + sin30°) = √ (1 + 1/2) = √ (3/2) = √6/2

B. cos75°-sin75° = √ (cos75°-sin75°) ² = √ (cos²75° - 2sin75°cos75° + sin²75°) =

= √ (1 - sin150°) = √ (1 - 1/2) = √ (1/2) = √2/2