Question

find the value of cos2pi/5 using the graph of cosx​

Answer 1

Answer:

How to prove cos2π5=−1+5√4

Step-by-step explanation:

Note that 2⋅2π5+3⋅2π5=2π, therefore cos(2⋅2π5)=cos(3⋅2π5). Put cos(2π5)=x. Using the formulas cos2x=2cos2x−1,cos3x=4cos3x−3cosx, we have 4x3−2x2−3x+1=0⇔(x−1)(4x2+2x−1)=0. Because cos(2π5)≠1, we get 4x2+2x−1=0. Another way, cos(2π5)>0, then cos2π5=−1+5–√2.

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