If tan -11-a-1-tan -11-x-tan -11-a2-x-1- then x isA- a3B a2-a-1C- a2-a-1D- a - 2

The correct option is B a2 a + 1We have, tan^ 11/a 1=tan^ 11/x+tan^ 11/a^2 x+1 ⇒1/a 1=a^2+1/(a^2+1).x x^2 1 ⇒ x^2 x(a^2 1)+1(a 1)(a^2+1)=0 (x^2 a^2) (a^2+1)( ...

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Byju's Answer

Standard XII

Mathematics

Property 1

If tan -11/a-...

Question

If $t a n^{- 1} \frac{1}{a - 1} = t a n^{- 1} \frac{1}{x} + t a n^{- 1} \frac{1}{a^{2} - x + 1}$ , then x is

a/2

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a³

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a² - a + 1

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a² + a - 1

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Solution

The correct option is C a² - a + 1
We have, $t a n^{- 1} \frac{1}{a - 1} = t a n^{- 1} \frac{1}{x} + t a n^{- 1} \frac{1}{a^{2} - x + 1}$
$\Rightarrow \frac{1}{a - 1} = \frac{a^{2} + 1}{(a^{2} + 1) . x - x^{2} - 1}$
$\Rightarrow x^{2} - x (a^{2} - 1) + 1 (a - 1) (a^{2} + 1) = 0$
$(x^{2} - a^{2}) - (a^{2} + 1) (x - a) = 0$
$(x - a) (x + a - a^{2} - 1) = 0$
$\Rightarrow∴ x = a$
or
$a^{2} - a + 1$

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If tan−11a−1=tan−11x+tan−11a2−x+1, then x is

The correct option is C a2 - a + 1We have, tan−11a−1=tan−11x+tan−11a2−x+1 ⇒1a−1=a2+1(a2+1).x−x2−1 ⇒x2−x(a2−1)+1(a−1)(a2+1)=0 (x2−a2)−(a2+1)(x−a)=0 (x−a)(x+a−a2−1)=0 ⇒∴x=a or a2−a+1

If $t a n^{- 1} \frac{1}{a - 1} = t a n^{- 1} \frac{1}{x} + t a n^{- 1} \frac{1}{a^{2} - x + 1}$ , then x is