Question

Express the ratios $\cos A$, $\tan A$ and $\sec A$ in terms of $\sin A$.

Answer 1

$\cos A=\sqrt{1-{\sin }^{2}A}\to \left(1\right)$

as, ${\cos }^2\theta +{\sin }^2\theta =1$

$\tan A=\frac{\sin A}{\cos A}$

$=\frac{\sin A}{\sqrt{1-{\sin }^{2}A}}$ ( from $\left(1\right)$ )

& $\sec A=\frac{1}{\cos A}$

$=\frac{1}{\sqrt{1-{\sin }^{2}A}}$ ( From $\left(1\right)$ )

so, $\cos A=\sqrt{1-{\sin }^{2}A},\tan A=\frac{\sin A}{\sqrt{1-{\sin }^{2}A}}$

& $\sec A=\frac{1}{\sqrt{1-{\sin }^{2}A}}$