Question

In an equilateral triangle ABC , match the following ratios to the values
$\begin{array}{cc}Trigonometricratios& Values\\ \left(i\right)tan{60}^{\circ }& \left(a\right)\frac{1}{\sqrt{3}}\\ \left(ii\right)cot{30}^{\circ }& \left(b\right)\sqrt{3}\\ \left(iii\right)cosec{30}^{\circ }& \left(c\right)2\\ \left(iv\right)sec{30}^{\circ }& \left(d\right)\frac{2}{\sqrt{3}}\end{array}$

• A. (i) -b , (ii) - b , (iii) - c , (iv) - d
• B. (i) -a , (ii) - b , (iii) - c , (iv) - d
• C. (i) -a , (ii) - b , (iii) - d , (iv) - c
• D. (i) -b , (ii) - a , (iii) - d , (iv) - c

Answer 1

The correct option is A (i) -b , (ii) - b , (iii) - c , (iv) - d

Let each side of the equilateral triangle be a.

Length of perpendicular AD =$\frac{\sqrt{3}a}{2}$

$tan60=tanB=\frac{AD}{BD}=\sqrt{3}$

$cot30=cot\left(\frac{A}{2}\right)=\frac{AD}{BD}=\sqrt{3}$

$cosec30=cosec\left(\frac{A}{2}\right)=\frac{AD}{BD}=2$

$sec30=sec\left(\frac{A}{2}\right)=\frac{AD}{BD}=\frac{2}{\sqrt{3}}$