Question

What is the value of

$\frac{tan30^\circ+cot30^\circ}{sec30^\circ+tan30^\circ}\times sin30^\circ$

• A. $$2-\sqrt{3}$$
• B. $$2+\sqrt{3}$$
• C. $$\frac{2}{3}$$
• D. $$\frac{-2}{3}$$

Answer 1

Answer:

$$\frac{2}{3}$$

Solution:

Calculation:

tan30^∘ = 1/√3 

cot30∘ = √3 

sec30∘ =  2/√3 

sin30∘ = 1/2

$\frac{tan30^\circ+cot30^\circ}{sec30^\circ+tan30^\circ}× sin30^\circ$

$\frac{{1\over\sqrt3}+\sqrt3}{{2\over\sqrt3}+{1\over\sqrt3}}$

⇒ {(1 + 3)/√3} / {(2 + 1)/√3} ×$\frac{1}{2}$

⇒ {4/√3} / {3/√3} ×$\frac{1}{2}$

⇒ 4/3 × 1/2

⇒ 2/3

∴ The correct answer is option (3).