10th Class Mathematics Introduction to Trigonometry Question Bank Case Based (MCQs) - Introduction to Trigonometry

The value of \[\sec x{}^\circ \] is:

A) \[\frac{\sqrt{91}}{6}\]

B) \[\frac{\sqrt{71}}{6}\]

C) \[\frac{\sqrt{41}}{4}\]

D) \[\frac{\sqrt{31}}{5}\]

Correct Answer: C

Solution :

We know the identity.

\[{{\sec }^{2}}x{}^\circ =1+{{\tan }^{2}}x{}^\circ =1+{{\left( \frac{5}{4} \right)}^{2}}=1+\frac{25}{16}=\frac{41}{16}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\sec x{}^\circ =\sqrt{\frac{41}{16}}=\frac{\sqrt{41}}{4}\]

So, option [c] is correct.