Question

$\frac{tan{55}^{\circ }}{cot{35}^{\circ }}\times sin{30}^{\circ }=A$

The value of 2A is ______.

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. 1
• D. 2

Answer 1

The correct option is C 1

Given that,
$\frac{tan{55}^{\circ }}{cot{35}^{\circ }}\times sin{30}^{\circ }=A\frac{tan{55}^{\circ }}{cot({90}^{\circ }-{55}^{\circ })}\times sin{30}^{\circ }=A$

$(\because tan(90-\theta )=cot\theta )$

$\Rightarrow \frac{tan{55}^{\circ }}{tan{55}^{\circ }}\times \frac{1}{2}=A\Rightarrow A=\frac{1}{2}\Rightarrow 2A=1$

Therefore, the value of 2A is 1.