Question : If $\operatorname{cosec} \theta=\frac{17}{15}$, then what will be the value of $\cos \theta?$
Option 1: $\frac{7}{17}$
Option 2: 1
Option 3: $\frac{8}{17}$
Option 4: $\frac{15}{17}$
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Correct Answer: $\frac{8}{17}$
Solution :
Given, $\operatorname{cosec} \theta=\frac{17}{15}$
⇒ $\sin \theta =\frac{1}{\operatorname{cosec} \theta}= \frac{15}{17}$
Now, $\cos \theta = \sqrt{1-\sin^2 \theta}$
⇒ $\cos \theta = \sqrt{1-(\frac{15}{17})^2}$
⇒ $\cos \theta = \sqrt{\frac{64}{289}}$
⇒ $\cos \theta = \frac{8}{17}$
Hence, the correct answer is $\frac{8}{17}$.
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