If tan-11-xa - b - -c - -1 x- - x - - 1-Find the value of a-b and c-

The correct option is C a=2, b=1, c=2 We know that, tan^ 11/√(x^2 1) = π/2 ^ 1 x Comparing this with the given #160; tan^ 11/√(x^a b) = ...

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Byju's Answer

Standard XII

Mathematics

Domain and Range of Basic Inverse Trigonometric Functions

If tan-11/√...

Question

If ${tan}^{- 1} \frac{1}{\sqrt{x^{a} - b}} = \frac{π}{c} - {sec}^{- 1} x$ , $| x | > 1$ .
Find the value of a,b and c.

a = 1, b = 1, c = 1

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a = 1, b = 2, c = 2

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a = 2, b = 2, c = 1

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a = 2, b = 1, c = 2

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Solution

The correct option is C $a = 2, b = 1, c = 2$
We know that, ${tan}^{- 1} \frac{1}{\sqrt{x^{2} - 1}} = \frac{π}{2} - {sec}^{- 1} x$
Comparing this with the given ${tan}^{- 1} \frac{1}{\sqrt{x^{a} - b}} = \frac{π}{c} - {sec}^{- 1} x$ , $| x | > 1$ .

We get the unknown parameter $a = 2, b = 1, c = 2$

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Similar questions

Q. If

{tan}^{- 1} (\frac{\sqrt{a + x} - \sqrt{b - x}}{\sqrt{b + x} + \sqrt{a - x}}) = \frac{π}{c} - \frac{1}{d} {cos}^{- 1} x

- \frac{1}{\sqrt{2}} \leq x \leq 1

. Find the value of a,b,c and d

Q. Show that:
(i)

\frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1

(ii)

{[\{\frac{x^{a (a - b)}}{x^{a (a + b)}}\} \div \{\frac{x^{b (b - a)}}{x^{b (b + a)}}\}]}^{a + b} = 1

(iii)

{(x^{\frac{1}{a - b}})}^{\frac{1}{a - c}} {(x^{\frac{1}{b - c}})}^{\frac{1}{b - a}} {(x^{\frac{1}{c - a}})}^{\frac{1}{c - b}} = 1

(iv)

{(\frac{x^{a^{2} + b^{2}}}{x^{a b}})}^{a + b} {(\frac{x^{b^{2} + c^{2}}}{x^{b c}})}^{b + c} {(\frac{x^{c^{2} + a^{2}}}{x^{a c}})}^{a + c} = x^{2 (a^{3} + b^{3} + c^{3})}

(v)

{(x^{a - b})}^{a + b} {(x^{b - c})}^{b + c} {(x^{c - a})}^{c + a} = 1

(vi)

{\{{(x^{a - a^{- 1}})}^{\frac{1}{a - 1}}\}}^{\frac{a}{a + 1}} = x

(vii)

{(\frac{a^{x + 1}}{a^{y + 1}})}^{x + y} {(\frac{a^{y + 2}}{a^{z + 2}})}^{y + z} {(\frac{a^{z + 3}}{a^{x + 3}})}^{z + x} = 1

(viii)

{(\frac{3^{a}}{3^{b}})}^{a + b} {(\frac{3^{b}}{3^{c}})}^{b + c} {(\frac{3^{c}}{3^{a}})}^{c + a} = 1

The solution set x= $\frac{(b_{1} c_{2} - b_{2} c_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ and y= $\frac{(c_{1} a_{2} - c_{2} a_{1})}{(a_{1} b_{2} - a_{2} b_{1})}$ to the pair of linear equations given below can be written as:

$a_{1}$ x + $b_{1}$ y + $c_{1}$ =0 and $a_{2}$ x + $b_{2}$ y + $c_{2}$ =0 .

Q. If

a + b + c = 1

a^{2} + b^{2} + c^{2}

a^{2} + b^{2} + c^{2} = 21

a b c = 8

. Find the value of

(1 - a) (1 - b) (1 - c)

Q. If

∣ ∣ ∣ ∣ ∣ \begin{matrix} a^{2} & b^{2} & c^{2} {(a + 1)}^{2} & {(b + 1)}^{2} & {(c + 1)}^{2} {(a - 1)}^{2} & {(b - 1)}^{2} & {(c - 1)}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = k (a - b) (b - c) (c - a)

, then find the value of

- k

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If tan−11√xa−b=πc−sec−1x, |x|>1.Find the value of a,b and c.

The correct option is C a=2,b=1,c=2We know that, tan−11√x2−1=π2−sec−1xComparing this with the given tan−11√xa−b=πc−sec−1x, |x|>1.We get the unknown parameter a=2,b=1,c=2

If ${tan}^{- 1} \frac{1}{\sqrt{x^{a} - b}} = \frac{π}{c} - {sec}^{- 1} x$ , $| x | > 1$ .
Find the value of a,b and c.