Answer to Question #122817 in Trigonometry for Ojugbele Daniel

Question #122817
If n is a positive integer, prove that (√3+1)^n +(√3-1)^n = 2^n+1 cosπn/6
1
Expert's answer
2020-07-01T17:26:11-0400

Given that n is a positive integer.

We have to prove

"( \\sqrt{3}+1 )^n +( \\sqrt{3}-1)^n= 2^{n+1} cos\\frac{\\pi n }{6}"

Question is wrong

Take "n=2" .

"L.H.S=(\\sqrt{3}+1)^2+(\\sqrt {3} -1)^2"


"=3+1+2\\sqrt{3}+3+1-2\\sqrt {3}"

"=8"

"R.H.S=2^{2+1} cos\\frac{ 2\\pi }{6}" "=2^3\u00d7\\frac{1}{2}=4"

Hence , "L.H.S \\neq R.H.S"



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