SSC IMD SA 2017 – Question 44

What is the value of 1/√3 Tan 45° + Cosec 60°?

• (√3 + 2)/2
• (√3 + 2)√3
• √3
• √3 + 2

Detailed Explanation:

We need to evaluate the trigonometric expression: $\frac{1}{\sqrt{3}} \tan 45^\circ + \operatorname{cosec} 60^\circ$.

Step-by-step Solution:

1. Standard Trigonometric Values:
   • $\tan 45^\circ = 1$
   • $\sin 60^\circ = \frac{\sqrt{3}}{2} \implies \operatorname{cosec} 60^\circ = \frac{1}{\sin 60^\circ} = \frac{2}{\sqrt{3}}$
2. Substitute these values into the expression:$$\text{Expression} = \left(\frac{1}{\sqrt{3}} \times 1\right) + \frac{2}{\sqrt{3}} = \frac{1}{\sqrt{3}} + \frac{2}{\sqrt{3}}$$
3. Combine the terms over the common denominator:$$\frac{1 + 2}{\sqrt{3}} = \frac{3}{\sqrt{3}} = \sqrt{3}$$
4. Official Key Note: Under standard algebraic simplification, the value evaluates to $\sqrt{3}$. In the official SSC IMD 2017 question paper and answer key, option a) $(\sqrt{3} + 2)/2$ was listed as the correct option (likely arising from a denominator misprint in the source question paper where $\sqrt{3}$ was printed as 2 or vice versa). Both the standard derivation ($\sqrt{3}$) and official key (Option a) are documented here.

Based on the official answer key, the marked answer is a) (√3 + 2)/2.