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MATHEMATICS · Multi-part · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Prove that: (i) tan⁡−117+tan⁡−1113=tan⁡−129\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{13}=\tan^{-1}\frac{2}{9} (ii) tan⁡−12+tan⁡−13=3π4\tan^{-1}2+\tan^{-1}3=\frac{3\pi}{4} (iii) tan⁡−112+tan⁡−115+tan⁡−118=π4\tan^{-1}\frac{1}{2}+\tan^{-1}\frac{1}{5}+\tan^{-1}\frac{1}{8}=\frac{\pi}{4} (iv) tan⁡−134+tan⁡−135−tan⁡−1819=π4\tan^{-1}\frac{3}{4}+\tan^{-1}\frac{3}{5}-\tan^{-1}\frac{8}{19}=\frac{\pi}{4} (v) tan⁡−115+tan⁡−117+tan⁡−113+tan⁡−118=π4\tan^{-1}\frac{1}{5}+\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{8}=\frac{\pi}{4}

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