Question

If $\sec \theta =\frac{13}{12}$, then $\tan \theta =.....$ and $\sin \theta =.....$

• A. $\frac{5}{12},\frac{5}{13}$
• B. $\frac{12}{13},\frac{13}{5}$
• C. $\frac{5}{12},\frac{12}{5}$
• D. None of these

Answer 1

Answer: (A)

$\frac{5}{12},\frac{5}{13}$

$\sec \theta =\frac{13}{12}\Rightarrow \cos \theta =\frac{1}{\sec \theta }=\frac{1}{\frac{13}{12}}=\frac{12}{13}$
Now using ${\sin }^2\theta +{\cos }^2\theta =1\Rightarrow {\sin }^2\theta +{\left(\frac{12}{13}\right)}^2=1\Rightarrow {\sin }^2\theta =\frac{25}{169}\Rightarrow \sin \theta =\frac{5}{13}$
so $\tan \theta =\frac{\sin \theta }{\cos \theta }=\frac{\frac{5}{13}}{\frac{12}{13}}=\frac{5}{12}$