MHT CET · Maths · Inverse Trigonometric Functions
If \(\tan ^{-1}(x+1)+\tan ^{-1} x+\tan ^{-1}(x-1)=\tan ^{-1} 3\), then for \(x < 0\) the value of \(500 x^4+270 x^2+997=\)
- A 6716
- B 1767
- C 1768
- D 6717
Answer & Solution
Correct Answer
(B) 1767
Step-by-step Solution
Detailed explanation
\(\tan ^{-1}(x+1)+\tan ^{-1}(x-1)=\tan ^{-1} 3-\tan ^{-1} x\) \(\tan ^{-1}\left(\frac{(x+1)+(x-1)}{1-(x+1)(x-1)}\right)=\tan ^{-1}\left(\frac{3-x}{1+3x}\right)\)
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