Multiple choice

If cos A, sin B, sin A, are in G.P then the roots of the equation $x^2 + 2x cot B + 1 = 0$ are

  1. Real and distinct

  2. real

  3. imaginary

  4. Real and Equal
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If cos A, sin B, sin A are in GP, then (sin B)^2 = cos A * sin A. The discriminant of x^2 + 2x cot B + 1 = 0 is D = (2 cot B)^2 - 4(1)(1) = 4(cot^2 B - 1). For real roots, D >= 0, so cot^2 B >= 1. This condition depends on the specific values of A and B, but given the options, 'real' is the standard answer for this type of problem.

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