Let a = cos 1° and b = sin 1°. We say that a real number is algebrai

1.	Let a = cos 1° and b = sin 1°. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then (A) a is algebraic but b is not algebraic (B) b is algebraic but a is not algebraic (C) both a and b are algebraic (D) neither a nor b is algebraic
Answer» Correct option (C) both a and b are algebraic Explanation: If cos 1° = p +√q (p, q ∈ Q) then it will be root of a quadratic equation whose other root is p – √q ⇒ cos 1° is algebraic ⇒ sin 1° is algebraic

Let a = cos 1° and b = sin 1°. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then (A) a is algebraic but b is not algebraic (B) b is algebraic but a is not algebraic (C) both a and b are algebraic (D) neither a nor b is algebraic

Answer»

Correct option (C) both a and b are algebraic

Explanation:

If cos 1° = p +√q (p, q ∈ Q)

then it will be root of a quadratic equation whose other root is p – √q

⇒ cos 1° is algebraic ⇒ sin 1° is algebraic

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Let a = cos 1° and b = sin 1°. We say that a real number is algebraic if it is a root of a polynomial with integer coefficients. Then (A) a is algebraic but b is not algebraic (B) b is algebraic but a is not algebraic (C) both a and b are algebraic (D) neither a nor b is algebraic

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