Question

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

Answer 1

The answer is
`\boxed {(1)/(2√(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

Answer 2

`(√(3) )/(6)`

Explanation:

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

tan60° =
`√(3)` , and

cot60° =
`(1)/(tan60)` =
`(1)/(√(3) )`

cos60° =
`(1)/(2)`

cot60° cos60°

=
`(1)/(√(3) )` ×
`(1)/(2)`

=
`(1)/(2√(3) )` ← rationalise the denominator by multiplying by
`(√(3) )/(√(3) )`

=
`(1)/(2√(3) )` ×
`(√(3) )/(√(3) )`

=
`(√(3) )/(6)`