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NDA 2022 Maths · Mathematics · Inverse Trigonometric Functions · hard

The value of tan ^-11/2+tan ^-11/5+tan ^-11/8 is

Single correct option

The value of tan⁡−112+tan⁡−115+tan⁡−118\tan^{-1}\dfrac12+\tan^{-1}\dfrac15+\tan^{-1}\dfrac18 is
  1. A. π4\dfrac\pi4
  2. B. π3\dfrac\pi3
  3. C. π2\dfrac\pi2
  4. D. π6\dfrac\pi6
Show answer and solution

Answer: (A) π4\dfrac\pi4

Since the products are small, tan⁡−112+tan⁡−115=tan⁡−17/109/10=tan⁡−179\tan^{-1}\frac12+\tan^{-1}\frac15=\tan^{-1}\frac{7/10}{9/10}=\tan^{-1}\frac79. Adding tan⁡−118\tan^{-1}\frac18: 7/9+1/81−7/72=65/7265/72=1\frac{7/9+1/8}{1-7/72}=\frac{65/72}{65/72}=1, so the sum is π4\frac\pi4.
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