Prove that tan⁻¹((2)/(11))+tan⁻¹((7)/(24))=tan⁻¹((1)/(2))

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\tan^{-1}\left(\dfrac{2}{11}\right)+\tan^{-1}\left(\dfrac{7}{24}\right)=\tan^{-1}\left(\dfrac{1}{2}\right)

Tamil Nadu DgeTamil Nadu HSC First Year (DGE) Commerce Board 2024Subjective· 3mImportance★★★★★

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Applying the addition formula to $\tan^{-1}\tfrac2{11}+\tan^{-1}\tfrac7{24}$ gives $\tan^{-1}\tfrac12$ .

Formula. For $AB<1$ , $\tan^{-1}A+\tan^{-1}B=\tan^{-1}\!\dfrac{A+B}{1-AB}.$ Here $A=\tfrac2{11},B=\tfrac7{24},\ AB=\tfrac{14}{264}=\tfrac{7}{132}<1.$

Numerator: $\ \dfrac2{11}+\dfrac7{24}=\dfrac{48+77}{264}=\dfrac{125}{264}.$

Denominator: $\ 1-\dfrac7{132}=\dfrac{125}{132}.$

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Q.Prove that $\tan^{-1}\left(\dfrac{2}{11}\right)+\tan^{-1}\left(\dfrac{7}{24}\right)=\tan^{-1}\left(\dfrac{1}{2}\right)$

Concept understanding — Compound Angle Formulae

Q.Prove that tan⁡−1(211)+tan⁡−1(724)=tan⁡−1(12)\tan^{-1}\left(\dfrac{2}{11}\right)+\tan^{-1}\left(\dfrac{7}{24}\right)=\tan^{-1}\left(\dfrac{1}{2}\right)tan−1(112​)+tan−1(247​)=tan−1(21​)

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Q.Prove that $\tan^{-1}\left(\dfrac{2}{11}\right)+\tan^{-1}\left(\dfrac{7}{24}\right)=\tan^{-1}\left(\dfrac{1}{2}\right)$

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