Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Express the ratios $\cos A ,$ tan $A$ and $\sec A$ in terms of $\sin A .$
Since,$\cos ^{2} A+\sin ^{2} A=1,$ therefore
$\cos ^{2} A =1-\sin ^{2} A , i . e ., \cos A =\pm \sqrt{1-\sin ^{2} A }$
This gives $\quad \cos A =\sqrt{1-\sin ^{2} A }$
Hence, $\quad \tan A =\frac{\sin A }{\cos A }=\frac{\sin A }{\sqrt{1-\sin ^{2} A }}$
and $\sec A =\frac{1}{\cos A }=\frac{1}{\sqrt{1-\sin ^{2} A }}$
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