Question

Find the value of cot 15°

Answer 1

Answer:

The value of cot 15° is $2+\sqrt{3}$.

Step-by-step explanation:

The given expression is

$\cot(15^{\circ})$

It can be written as

$\cot(15^{\circ})=\cot(45^{\circ})-30^{\circ})$

$\cot(15^{\circ})=\frac{\cot(45)\cot (30)+1}{\cot(30)-\cot (45)}$

$\cot(15^{\circ})=\frac{(1)(\sqrt{3})+1}{\sqrt{3}-1}$

$\cot(15^{\circ})=\frac{\sqrt{3}+1}{\sqrt{3}-1}$

Multiply both numerator and denominator by $(\sqrt{3}+1)$.

$\cot(15^{\circ})=\frac{\sqrt{3}+1}{\sqrt{3}-1}\times \frac{\sqrt{3}+1}{\sqrt{3}+1}$

$\cot(15^{\circ})=\frac{(\sqrt{3}+1)^2}{(\sqrt{3})^2-1^2}$

$\cot(15^{\circ})=\frac{(3+1+2\sqrt{3}}{3-1}$

$\cot(15^{\circ})=\frac{(2(2+\sqrt{3})}{2}=2+\sqrt{3}$

Therefore the value of cot 15° is $2+\sqrt{3}$.

Answer 2

Answer:

2+root3

this is the answer i am not able to put root symbol sorry