Keep Thinking
Algebra
Level
1
Which of the following is rational? (all the angles are in degree)
cos3
none of these
cos2
cos7
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1 solution
Let cosα € R- Q ((real numbers – rational numbers are irrational numbers)say K 2cos^2(α)-1€ K, Cos2α€ K, Cos3α€ K ,thus cosnα €K. Hence cos2 € K but cos30 € Q (contradiction). for cos3 same reason Cos7 € K => cos(7t) € K but cos210 € Q (contradiction)