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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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manish

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