Question

demonstram egalitatea:
a)cosπ/5+cos3π/5=1/2

Answer 1

  cosA + cosB = 2cos[(A+B)/2] cos[(A-B)/2]
=> cos(π/5) + cos(3π/5)
= 2cos(2π/5) cos(π/5)
= 2cos(π/5) sin(π/5) cos(2π/5) / sin(π/5) ... [ înmulțirea numărătorul și numitorul sin(π/5)]
= sin(2π/5) cos(2π/5) / sin(π/5)
= 2sin(2π/5) cos(2π/5) / 2sin(π/5)
= sin(4π/5) / 2sin(π/5)
= sin(π - π/5) / 2sin(π/5)
= sin(π/5) / 2sin(π/5)
= 1/2.