Prove that:tan−131+tan−151+tan−171+tan−181=4π

Question

Prove that:tan−131​+tan−151​+tan−171​+tan−181​=4π​

Filo · Accepted Answer

As we know thattan−1a+tan−1b=tan−11−aba+b​,ab<1So tan−131​+tan−151​+tan−171​+tan−181​=tan−11−31​×51​31​+51​​+tan−11−71​×81​71​+81​​                                                                               =tan−174​+tan−1113​                                                                              =tan−11−74​×113​74​+113​​                                                                             =tan−11=4π​∴tan−131​+tan−151​+tan−171​+tan−181​=4π​Hence Proved

Question Text	Prove that: $tan^{- 1} \frac{1}{3} + tan^{- 1} \frac{1}{5} + tan^{- 1} \frac{1}{7} + tan^{- 1} \frac{1}{8} = \frac{π}{4}$
Answer Type	Text solution:1
Upvotes	150

Prove that:
$tan^{- 1} \frac{1}{3} + tan^{- 1} \frac{1}{5} + tan^{- 1} \frac{1}{7} + tan^{- 1} \frac{1}{8} = \frac{π}{4}$

Text solutionVerified

Practice questions from similar books

Prove that:tan−131​+tan−151​+tan−171​+tan−181​=4π​

Text solutionVerified

Practice questions from similar books

Prove that:
$tan^{- 1} \frac{1}{3} + tan^{- 1} \frac{1}{5} + tan^{- 1} \frac{1}{7} + tan^{- 1} \frac{1}{8} = \frac{π}{4}$