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# Write all the other trigonometric ratios of angle A in terms of sec A.

2.    Write all the other trigonometric ratios of $\angle A$  in terms of $\sec A$.

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We know that the identity $\sin^2 A + \cos^2 =1$
$\\\sin^2 A =1- \cos^2 \\ sin^2A = 1-\frac{1}{\sec^2A}$
$=\frac{\sec^2A -1}{\sec^2A}$
$\sin A =\sqrt{\frac{\sec^2A -1}{\sec^2A}}$
$=\frac{{}\sqrt{\sec^2A -1}}{\sec A}$

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

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

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

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