Question

Write tge value of tan^-1(a/b) -tan^-1((a-b)/(a+b))

Answer 1

$The \: \: answer \: \: is \: \: given \: \: below \\ \\ {tan}^{ - 1} ( \frac{a}{b} ) - {tan}^{ - 1} (\frac{a - b}{a + b}) \\ \\ = {tan}^{ - 1} \frac{ \frac{a}{b} - \frac{a - b}{a + b} }{1 + ( \frac{a}{b} \times \frac{a - b}{a + b} ) } \\ \\ = {tan}^{ - 1} \frac{ \frac{a(a + b) - b(a - b)}{b(a + b)} }{ \frac{b(a + b) + a(a - b)}{b(a + b)} } \\ \\ = {tan}^{ - 1} \frac{ {a}^{2} + ab - ab + {b}^{2} }{ab + {b}^{2} + {a}^{2} - ab} \\ \\ = {tan}^{ - 1} \frac{ {a}^{2} + {b}^{2} }{ {a}^{2} + {b}^{2} } \\ \\ = {tan}^{ - 1} (1) \\ \\ = \frac{\pi}{4} \\ \\ Thank \: \: you \: \: for \: \: your \: \: question.$