Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
Write all the other trigonometric ratios of $\angle A$ in terms of $\sec$ $A$.
We know that,
$\cos A=\frac{1}{\sec A}$
Also, $\sin ^{2} A+\cos ^{2} A=1$
$\sin ^{2} A=1-\cos ^{2} A$
$\sin A=\sqrt{1-\left(\frac{1}{\sec A}\right)^{2}}$
$=\sqrt{\frac{\sec ^{2} A-1}{\sec ^{2} A}}=\frac{\sqrt{\sec ^{2} A-1}}{\sec A}$
$\tan ^{2} A+1=\sec ^{2} A$
$\tan ^{2} A=\sec ^{2} A-1$
$\tan A =\sqrt{\sec ^{2} A -1}$
$\cot A =\frac{\cos A }{\sin A } =\frac{\frac{1}{\sec A}}{\frac{\sqrt{\sec ^{2} A-1}}{\sec A}}$
$=\frac{1}{\sqrt{\sec ^{2} A-1}}$
$\operatorname{cosec} A =\frac{1}{\sin A }=\frac{\sec A }{\sqrt{\sec ^{2} A -1}}$
Similar Questions
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Express $\sin 67^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$
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Given $\tan A=\frac{4}{3},$ find the other trigonometric ratios of the $\angle A$
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Express $\cot 85^{\circ}+\cos 75^{\circ}$ in terms of trigonometric ratios of angles between $0^{\circ}$ and $45^{\circ}$
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Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.
$\sqrt{\frac{1+\sin A }{1-\sin A }}=\sec A +\tan A$