If tan -1 x -3- x -tan -1 x -3- x -tan -16- x - then the value of 5 x 8-4 x 4-7 equalsA- 376B- 393C- 379D- 397

The correct option is A 376 We have tan^ 1 ( x+3/x ) tan^ 1 ( x 3/x )=tan^ 1 (6/x ) ⇒ tan^ 1 ( ( x+3/x ) ( x 3/x )/1+ ( x+3/x ) ( x 3/x ) )=tan^ 16/x ⇒ x^2 9 ...

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Standard XII

Mathematics

First Principle of Differentiation

If tan -1 x +...

Question

If $t a n^{- 1} (x + \frac{3}{x}) - t a n^{- 1} (x - \frac{3}{x}) = t a n^{- 1} (\frac{6}{x})$ , then the value of $5 x^{8} - 4 x^{4} + 7$ equals

397

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393

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376

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379

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Solution

The correct option is C
376

We have $t a n^{- 1} (x + \frac{3}{x}) - t a n^{- 1} (x - \frac{3}{x}) = t a n^{- 1} (\frac{6}{x}) \Rightarrow t a n^{- 1} (\frac{(x + \frac{3}{x}) - (x - \frac{3}{x})}{1 + (x + \frac{3}{x}) (x - \frac{3}{x})}) = t a n^{- 1} \frac{6}{x} \Rightarrow x^{2} - \frac{9}{x^{2}} = 0 \Rightarrow x^{4} = 9$
Hence, $(5 x^{8} - 4 x^{4} + 7) = 5 (81) - 4 (9) + 7 = 405 - 36 + 7 = 412 - 36 = 376$

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If tan−1(x+3x)−tan−1(x−3x)=tan−1(6x), then the value of 5x8−4x4+7 equals

The correct option is C 376 We have tan−1(x+3x)−tan−1(x−3x)=tan−1(6x)⇒tan−1((x+3x)−(x−3x)1+(x+3x)(x−3x))=tan−16x⇒x2−9x2=0⇒x4=9 Hence, (5x8−4x4+7)=5(81)−4(9)+7=405−36+7=412−36=376

If $t a n^{- 1} (x + \frac{3}{x}) - t a n^{- 1} (x - \frac{3}{x}) = t a n^{- 1} (\frac{6}{x})$ , then the value of $5 x^{8} - 4 x^{4} + 7$ equals