Question

cos(11n/12)+cos(5n/12)

Answer 1

Ответ:

-√2/2.

Пошаговое объяснение:

соs a + cos b = 2•cos((a+b)/2)•cos((a-b)/2);

В нашем случае

сos(11π/12)+cos(5π/12) =

2cos((11π/12 +5π/12)/2•cos((11π/12 -5π/12)/2 =

2cos(16π/24)•cos(6π/24) = 2cos(2π/3)•cos(π/4) = 2cos(π - π/3)•cos(π/4) = -2•cos(π/3)•cos(π/4) = -2•1/2•√2/2 = -√2/2.