Question 141

If sec$$\theta=\frac{13}{12}\ and\ \theta\ $$is acute, then what is the value of $$(\sqrt{cot\theta+tan \theta})$$?

Solution

Given,

sec$$\theta = \frac{13}{12}$$

Then, cot$$\ \theta = \frac{12}{5}$$ and tan$$\ \theta = \frac{5}{12}$$

$$(\sqrt{cot\theta+tan \theta})$$ = $$(\sqrt{\frac{12}{5}+\frac{5}{12}})$$ = $$(\sqrt{\frac{169}{60}})$$ = $$\frac{13}{2\sqrt{15}}$$

Hence, option A is the correct answer.

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