Question

If csc theta = 8/7, which equation represents (cot theta) ?

Answer 1

Out of the given choice, the equation represents $\cot \theta=\frac{\sqrt{15}}{7}$.

Answer: Option B

Step-by-step explanation:

We know, $\csc \theta=\frac{1}{\sin \theta}$

                $\sin \theta=\frac{1}{\csc \theta}$

Given data:

                $\csc \theta=\frac{8}{7}$

So, now sin theta can express as

                $\sin \theta=\frac{7(\text { opposite })}{8(\text { Hypotenuse })}$

Sin theta defined by the ratio of opposite to the hypotenuse. In general, the adjacent can be calculated by,

           $\text {(opposite) }^{2}+(\text { adjacent })^{2}=(\text {Hypotenuse})^{2}$

          $7^{2}+(\text { adjacent })^{2}=8^{2}$

         $(\text {adjacent})^{2}=8^{2}-7^{2}=64-49=15$

Taking square root, we get

           $\text { adjacent }=\sqrt{15}$

Also, we know the formula for cot theta,

         $\cot \theta=\frac{1}{\tan \theta}=\frac{1}{\left(\frac{\sin \theta}{\cos \theta}\right)}=\frac{\cos \theta}{\sin \theta}$

Cos theta denoted as the ratio of adjacent to the hypotenuse.

           $\cos \theta=\frac{\sqrt{15}(\text {Adjacent})}{8(\text {Hypotenuse})}$

Therefore, find now as below,

           $\cot \theta=\frac{\left(\frac{\sqrt{15}}{8}\right)}{\left(\frac{7}{8}\right)}=\frac{\sqrt{15}}{8} \times \frac{8}{7}=\frac{\sqrt{15}}{7}$

Answer 2

Answer:

Option B

Step-by-step explanation:

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