अगर $sin 17^{circ}=frac{x}{y}$, तो $sec 17^{circ}-sin$ $73^{circ}$ का मूल्य

है:

sec17° – sin73° = sec17° – sin (90° – 17°) = sec17° – cos17° $=frac{1}{cos 17^{circ}}-cos 17^{circ}=frac{1-cos ^{2} 17^{circ}}{cos 17^{circ}}=frac{sin ^{2} 17}{cos 17^{circ}}$ $=frac{frac{x^{2}}{y^{2}}}{sqrt{1-frac{x^{2}}{y^{2}}}}=frac{frac{x^{2}}{y^{2}}}{frac{sqrt{y^{2}-x^{2}}}{y}}=frac{x^{2}}{y sqrt{y^{2}-x^{2}}}$ Alternative:

$sin 17^{circ}=frac{x}{y}=frac{p}{h}$

$ecause(h)^{2}=(b)^{2}+(p)^{2}$

Base $=sqrt{mathrm{h}^{2}-p^{2}}$

$=sqrt{y^{2}-x^{2}}$

$sec 17^{circ}-sin 73^{circ}$

$=frac{h}{p}-frac{p}{mathrm{~h}}$

$=frac{y}{sqrt{y^{2}-x^{2}}}-frac{sqrt{y^{2}-x^{2}}}{y}$

$=frac{y^{2}-y^{2}+x^{2}}{y sqrt{y^{2}-x^{2}}}=frac{x^{2}}{y sqrt{y^{2}-x^{2}}}$