Let a tan - 1 x + cot - 1 x + sin - 1 x b . If and denote the minimum and maximum possible values of a and b respectively, then:

Question

Let $a \leq \tan^{- 1} x + \cot^{- 1} x + \sin^{- 1} x \leq b .$ If $α$ and $β$ denote the minimum and maximum possible values of $a$ and $b$ respectively, then:

Smart Achievers · Accepted Answer

(1)

Ans. $α = 0, β = π$

Explanation:

We know that

$\tan^{- 1} x + \cot^{- 1} x = \frac{π}{2}$

$\tan^{- 1} x + \cot^{- 1} x + \sin^{- 1} x = \frac{π}{2} + \sin^{- 1} x$

$\frac{- π}{2} \leq \sin^{- 1} x \leq \frac{π}{2}$

$\Rightarrow - \frac{π}{2} + \frac{π}{2} \leq \sin^{- 1} x + \frac{π}{2} \leq \frac{π}{2} + \frac{π}{2}$

$\Rightarrow 0 \leq \frac{π}{2} + \sin^{- 1} x \leq π$

$\Rightarrow 0 \leq \tan^{- 1} x + \cot^{- 1} x + \sin^{- 1} x \leq π$

$∴$ $α = 0, β = π$

Solution

Q.
Let $a \leq \tan^{- 1} x + \cot^{- 1} x + \sin^{- 1} x \leq b .$ If $α$ and $β$ denote the minimum and maximum possible values of $a$ and $b$ respectively, then:

1 $α = 0, β = π$

2 $α = 0, β = \frac{π}{2}$

3 $α = \frac{π}{2}, β = π$

4 $α = - \frac{π}{2}, β = \frac{π}{2}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. Let a≤tan-1x+cot-1x+sin-1x≤b. If α and β denote the minimum and maximum possible values of a and b respectively, then:

1 α=0, β=π

2 α=0, β=π2

3 α=π2, β=π

4 α=-π2, β=π2