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P r ove tha t 2 tan^-1(1/5) + tan^-1(1/8) = tan ^-1(4/7)

Prove that 2 tan^-1(1/5) + tan^-1(1/8) =  tan^-1(4/7)

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
Hello Student,
Please find answer to your question below

A = 2tan^{-1}\frac{1}{5} + tan^{-1}\frac{1}{8}
A = tan^{-1}\frac{1}{5}+tan^{-1}\frac{1}{5} + tan^{-1}\frac{1}{8}
tan^{-1}x + tan^{-1}y = tan^{-1}(\frac{x+y}{1-xy})
A = tan^{-1}\frac{1}{5}+(tan^{-1}\frac{1}{5} + tan^{-1}\frac{1}{8})
A = tan^{-1}\frac{1}{5}+(tan^{-1}\frac{\frac{1}{5}+\frac{1}{8}}{1-\frac{1}{5}.\frac{1}{8}})
A = tan^{-1}\frac{1}{5}+(tan^{-1}\frac{\frac{13}{40}}{\frac{39}{40}})
A = tan^{-1}\frac{1}{5}+(tan^{-1}\frac{1}{3})
A = (tan^{-1}\frac{1}{5}+tan^{-1}\frac{1}{3})
A = (tan^{-1}\frac{\frac{1}{5}+\frac{1}{3}}{1-\frac{1}{5}.\frac{1}{3}}})
A = (tan^{-1}\frac{\frac{8}{15}}{\frac{14}{15}})
A = (tan^{-1}\frac{8}{14})
A = tan^{-1}\frac{4}{7}

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