Question

How can we say that for small displacement sin theta is equal to tan theta?

Answer 1

$sinx = x - \frac{ {x}^{ 3} }{6} + \frac{ {x}^{5} }{120} - ......... \\ \\ tanx \: = \: x + \frac{ {x}^{3} }{3} + \frac{2 {x}^{5} }{15} + ............ \\ \\ now \: for \: x < < 1 \\ \\ si nx \: = \: x \\ \\ tan \: x \: = \: x \\ \\ therefore \\ \\ \large{ \bold{ for\: x < < 1}} \\ \\ \large{ \bold{sin \: x = tan \: x \: = x}}$

hope it helps.