# Write all the other trigonometric ratios of $\angle \mathrm{A}$ in terms of $\sec \mathrm{A}$.

Question.

Write all the other trigonometric ratios of $\angle \mathrm{A}$ in terms of $\sec \mathrm{A}$.

Solution:

(i) $\sin A=\sqrt{1-\cos ^{2} A}$

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

(ii) $\cos A=\frac{1}{\sec A}$

(iii) $\tan A=\sqrt{\sec ^{2} \mathbf{A}-\mathbf{1}}$

(iv) $\cot A=\frac{1}{\tan A}=\frac{1}{\sqrt{\sec ^{2} A-1}}$

(v) $\operatorname{cosec} A=\frac{1}{\sin A}=\frac{\sec A}{\sqrt{\sec ^{2} A-1}}$

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