Question

Evaluate Cos 60° + Sec 30°​

Answer 1

Trigonometry

To solve these types of questions, use the concept listed below:

• Trigonometric ratios: They are sin, cos, tan, cot, sec, cosec.
• The standard angles of these trigonometric ratios are 0°, 30°, 45°, 60° and 90°.

Analyse the values of important angles for all the six trigonometric ratios shown in the table given below:

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

[Check the attachment if any case you're not able to see the table]

Let's head to the Question now:

$\implies \cos(60^\circ) + \sec(30^\circ) \\ \\ \implies \frac{1}{2} + \frac{2}{ \sqrt{3} } \\ \\ \implies \frac{1}{2} + \frac{2 \sqrt{3} }{3} \\ \\ \implies \boxed{\frac{3 + 4 \sqrt{3} }{6} }$

Hence, this is our required answer.