Question 57

If $$\cot \theta = \frac{80}{39},$$ find the value of $$cosec \theta$$.

Solution

Given, $$\cot \theta = \frac{80}{39}$$

$$\therefore\ $$ $$\operatorname{cosec}\theta=\sqrt{1+\cot^2\theta\ }$$

$$=\sqrt{1+\left(\frac{80}{39}\right)^2}$$

$$=\sqrt{1+\frac{6400}{1521}}$$

$$=\sqrt{\frac{1521+6400}{1521}}$$

$$=\sqrt{\frac{7921}{1521}}$$

$$=\frac{89}{39}$$

Hence, the correct answer is Option A

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