Question

If $\sin A=\frac{1}{3}$ , then $\cos A\text{cosec}A+\tan A\sec A=$

Answer 1

Given,

$\sin A=\frac{1}{3}$

$\cos A=\sqrt{1-{\sin }^{2}A}=\sqrt{1-\frac{1}{3^2}}$

$\therefore \cos A=\frac{2\sqrt{2}}{3}$

Let $Z=\cos AcosecA+\tan A\sec A$

$=\frac{\cos A}{\sin A}+\frac{\sin A}{{\cos }^{2}A}$

$=\frac{\frac{2\sqrt{2}}{3}}{\frac{1}{3}}+\frac{\frac{1}{3}}{{\left(\frac{2\sqrt{2}}{3}\right)}^2}$

$Z=\frac{16\sqrt{2}+3}{8}$