For what value of `theta` the percentage error in the measurement of a physical quantity given by `m= ktan theta` is minimum where k is a constant.

Answer

`45^(@)`

Explanation

`:' m=k tan theta`
`:. Dm= k sec^(2) theta d theta`
`rArr (dm)/m=(k sec^(2) theta)/(k tan theta) d theta`
`rArr (dm)/m=(d theta)/(sin theta cos theta)=(2d theta)/(sin 2theta)`
`rArr %` error is minimum when `sin 2 theta`
has maximum value hence `2theta=pi/2` or `theta=45^(@)`