Question

Find the value of cot х.

Answer 1

Given:

Right-angled triangle with hypotenuse equal to 2 and perpendicular equal to square root of 3 with respect to angle x.

Formula:

\[\text{Base}^2 + \text{Perpendicular}^2 = \text{Hypotenuse}^2 \text{ and } \cot x = \frac{\text{Base}}{\text{Perpendicular}}\]

Solution:

\[\text{Base}^2 + (\sqrt{3})^2 = 2^2\]  [Applying Pythagoras theorem to the right-angled triangle]

Base² + 3 = 4  [Squaring the perpendicular and hypotenuse lengths]

Base² = 4 − 3  [Transposing terms to solve for base squared]

Base² = 1  [Subtracting 3 from 4]

Base = 1  [Taking the positive square root of both sides]

\[\cot x = \frac{1}{\sqrt{3}}\]  [Substituting the values of base and perpendicular into the cotangent ratio]

\[\therefore {\cot x = \frac{1}{\sqrt{3}}}\]