Question

the percentage error in measurement of a physical quantity y, given by y=$\pi$tanx

Answer 1

$y= \pi\ tan\ x\\\\ \frac{dy}{dx} = \pi\ Sec^2x\\\\ \Delta y=\pi\ Sec^2x\ \Delta x\\\\ \frac{\Delta y}{y}=\frac{\pi\ Sec^2x\ \Delta x}{\pi\ tan\ x}\\\\\frac{\Delta y*100}{y}=\frac{100*\Delta x}{Cos^2x\ tan\ x}\\\\=\frac{100\Delta x}{Cosx\ Sin\ x}=\frac{200\Delta x}{Sin\ 2x}\\=\frac{2x}{Sin\ 2x} *\frac{ 100*\Delta x}{x}\\\\percentage\ error\ in\ y=\frac{2x}{Sin\ 2x} * percentage\ error\ in\ x.$

If x is small, then Sin 2x = 2x.
 
 Then percentage error in y = % error in x

Answer 2

Answer:

Explanation:we just need to differentiate and put the value of sin 2 theta.