Question

Help, I don’t know what I’m doing
Trigonometry

Answer 1

Answer:

$\frac{\sqrt{3} }{6}$

Step-by-step explanation:

using the 30- 60- 90 triangle for exact values , then

tan60° = $\sqrt{3}$ , and

cot60° = $\frac{1}{tan60}$ = $\frac{1}{\sqrt{3} }$

cos60° = $\frac{1}{2}$

cot60° cos60°

= $\frac{1}{\sqrt{3} }$ × $\frac{1}{2}$

= $\frac{1}{2\sqrt{3} }$ ← rationalise the denominator by multiplying by $\frac{\sqrt{3} }{\sqrt{3} }$

= $\frac{1}{2\sqrt{3} }$ × $\frac{\sqrt{3} }{\sqrt{3} }$

= $\frac{\sqrt{3} }{6}$

Answer 2

The answer is $\boxed {\frac{1}{2\sqrt{3}}}$

The needed trigonometric values :

• The value of cot 60° = 1/√3
• The value of cos 60° = 1/2

Hence, the value of the expression is :

• cot 60° × cos 60°
• 1/√3 × 1/2
• 1/2√3