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8. Introduction to Trigonometry
easy
$\cos \theta=\frac{15}{17},$ then the value of $\operatorname{cosec} \theta+\cot \theta $ is .........
A
$\frac{1}{4}$
B
$\frac{7}{17}$
C
$4$
D
$\frac{7}{8}$
Solution
$\sin ^{2} \theta=1-\cos ^{2} \theta=1-\left(\frac{15}{17}\right)^{2}=1-\frac{225}{289}=\frac{64}{289}=\left(\frac{8}{17}\right)^{2} \quad \therefore \sin \theta=\frac{8}{17}$
From this, $\operatorname{cosec} \theta=\frac{17}{8}$ and $\cot \theta=\frac{\cos \theta}{\sin \theta}=\frac{15 / 17}{8 / 17}=\frac{15}{8}$
Now, $\operatorname{cosec} \theta+\cot \theta=\frac{17}{8}+\frac{15}{8}=\frac{32}{8}=4$
Standard 10
Mathematics
