If - -2- - and - then which one of the following is true-

The correct option is B e^cos β cos α lt; β/αLet f(x) = e^cos x/x f'(x) = x sin e^cos x e^cos x/x^2 = e^cos x/x^2 (x sin x + 1) ∴ f(x) is decreasing ...

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Standard XII

Mathematics

Polar Representation of a Complex Number

If α, β∈π/2, ...

Question

If $α, β ϵ (\frac{π}{2}, π)$ and $α < β$ , then which one of the following is true?

e^{c o s α - c o s β} < \frac{α}{β}

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e^{c o s β - c o s α} < \frac{β}{α}

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e^{c o s α - c o s β} < \frac{β}{α}

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e^{c o s β - c o s α} < \frac{α}{β}

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Solution

The correct option is B $e^{c o s β - c o s α} < \frac{β}{α}$
$L e t f (x) = \frac{e^{c o s x}}{x} f^{'} (x) = \frac{- x s i n e^{c o s x} - e^{c o s x}}{x^{2}} = \frac{- e^{c o s x}}{x^{2}} (x s i n x + 1)$
$∴ f (x)$ is decreasing function in $(\frac{π}{2}, π)$
$∴ f (β) < f (α)$

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If α,βϵ(π2,π) and α<β, then which one of the following is true?

The correct option is B ecos β−cos α<βαLet f(x)=ecosxxf′(x)=−x sin ecos x−ecos xx2=−ecos xx2(x sinx+1) ∴f(x) is decreasing function in (π2,π) ∴f(β)<f(α)

If $α, β ϵ (\frac{π}{2}, π)$ and $α < β$ , then which one of the following is true?

The correct option is B $e^{c o s β - c o s α} < \frac{β}{α}$
$L e t f (x) = \frac{e^{c o s x}}{x} f^{'} (x) = \frac{- x s i n e^{c o s x} - e^{c o s x}}{x^{2}} = \frac{- e^{c o s x}}{x^{2}} (x s i n x + 1)$
$∴ f (x)$ is decreasing function in $(\frac{π}{2}, π)$
$∴ f (β) < f (α)$