If A=cos2x+cos2x1,B=cosx−cosx1 ∀x=(2n±1)2π, then the minimum value of BA is

BA=cosx−cosx1cos2x+cos2x1=(cosx−cosx1)(cosx−cosx1)2+2=(cosx−cosx1)+(cosx−cosx1)2BA=B+B2≥22

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If A=^{2}x+{1}{^{2}x},B=:x-{1}{:x} :x:(2n 1){}{2}, then the

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If $A = cos^{2} x + \frac{1}{cos ^{2} x}, B = cos x - \frac{1}{cos x} \forall x \neq = (2 n \pm 1) \frac{π}{2}$ , then the minimum value of $\frac{A}{B}$ is

2

22

\frac{1}{2}

None of these

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Levi Discussed

A = cos^{2} x + \frac{1}{cos ^{2} x}, B = cos x - \frac{1}{cos x} \forall x \neq = (2 n \pm 1) \frac{π}{2}

, then the minimum value of

\frac{A}{B}

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\frac{A}{B} = \frac{cos ^{2} x + \frac{1}{cos ^{2} x}}{cos x - \frac{1}{cos x}} = \frac{( cos x - \frac{1}{cos x} ) ^{2} + 2}{( cos x - \frac{1}{cos x} )}

= (cos x - \frac{1}{cos x}) + \frac{2}{( cos x - \frac{1}{cos x} )}

\frac{A}{B} = B + \frac{2}{B} \geq 22

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Question Text	If $A = cos^{2} x + \frac{1}{cos ^{2} x}, B = cos x - \frac{1}{cos x} \forall x \neq = (2 n \pm 1) \frac{π}{2}$ , then the minimum value of $\frac{A}{B}$ is
Answer Type	Text solution:1
Upvotes	151