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The percentage error in measurement of a...

The percentage error in measurement of a physical quantity m, given by `m=pi tan theta`, is minimum when

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The correct Answer is:
`45^(@)`
`:' 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^(@)`
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