ABC Isosceles triangle has its head A Where the angle ABC = 2π/5
and k is a relative integer , we put BC=a .
Bisector of the angle ABC cut the line segment [AC] In point D.
[DH],[DI],[AJ] and [BK] Are the elevations in the triangles DAB , DBC , ABC , DBC Respectively.
1. complete the shape.
a. Prove that the two triangles DAB and DBC are Isosceles.
b.Consider the triangle, Express length AB a function of cos(π/5) and a , Infer the phrase CD a function of cos(π/5) and a
c. Express the triangle DBC , Proved that, CD=2a cos(2π/5)
d. Infer that cos(π/5)-cos(2π/5)=1/2
a. Express the triangle DBC , Express length IB a function of cos(π/5) and a , Infer the phrase CD a function of cos(π/5) and a
b. Prove that IC= 2a [cos²(2π/5)]
c. Infer that cos(π/5)+cos²(2π/5)=1
a. Solve in ℝ the following equation: x²+1/2 x-1/4
b. Check that cos(π/5) is a solution to this equation
c. Prove that for every real number x it is: cos(sinx)>sin(cosx)