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Q-solve-if-t-2-n-2-cos-2-x-m-2-sin-2-x-then-show-that-t-d-2-t-dx-2-nm-2-t-3-




Question Number 79512 by M±th+et£s last updated on 25/Jan/20
Q.solve  if t^2 =n^2 cos^2 (x)+m^2 sin^2 (x)    then show that:  t+(d^2 t/dx^2 )=(((nm)^2 )/t^3 )
$${Q}.{solve} \\ $$$${if}\:{t}^{\mathrm{2}} ={n}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({x}\right)+{m}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$$${then}\:{show}\:{that}: \\ $$$${t}+\frac{{d}^{\mathrm{2}} {t}}{{dx}^{\mathrm{2}} }=\frac{\left({nm}\right)^{\mathrm{2}} }{{t}^{\mathrm{3}} } \\ $$$$ \\ $$

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