Prove that \(\displaystyle{\sin{{\frac{{\pi}}{{{14}}}}}}\) is a root of

Dominique Pace

Dominique Pace

Answered question


Prove that sinπ14 is a root of 8x34x24x+1=0

Answer & Explanation

Harry Gibson

Harry Gibson

Beginner2022-04-01Added 13 answers

Use the sine's definition in terms of complex exponentials:
Then recall that (a+b)3=a3+3a2b+3ab2+b3 and (a+b)2=a2+2ab+b2
And (2i)3=8i and (2i)2=4 and 1i=i
Then turn the crank.

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