What is componendo - dividendo - Maths - Trigonometric Functions

Question

What is componendo - dividendo??

Shridhar Kaushik · Accepted Answer

Componendo and dividendo is a method of simplification in Mathematics According to it, $i f \frac{a}{b} = \frac{c}{d} a n d a \neq b, c \neq d T h e n, \frac{a + b}{a - b} = \frac{c + d}{c - d}$ This proof is invalid for a=b and c=d because if $frac{a}{b} = frac{c}{d}$ such that a = b and c = d then by application of componendo and dividendo, we get - $\frac{a + b}{a - b} = \frac{c + d}{c - d} \Rightarrow \frac{a + b}{0} = \frac{c + d}{0}$ [as a=b and c=d] Since division by zero is not defined So, this proof is invalid for a = b and c = d