Question 54

If $$cosec A = \frac{25}{7}$$, then what is the value of Tan A?

Solution

Given, $$\operatorname{cosec}A=\frac{25}{7}$$

$$=$$> $$\sin A=\frac{7}{25}$$

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

$$=\sqrt{1-\left(\frac{7}{25}\right)^2}$$

$$=\sqrt{1-\frac{49}{625}}$$

$$=\sqrt{\frac{625-49}{625}}$$

$$=\sqrt{\frac{576}{625}}$$

$$=\frac{24}{25}$$

$$\therefore\ \tan A=\frac{\sin A}{\cos A}=\frac{\frac{7}{25}}{\frac{24}{25}}=\frac{7}{24}$$

Hence, the correct answer is Option B

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