Question

найдите значение выражений
A.sin15+cos15
B. cos75-sin75

Answer 1

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