Question

What is the value of Cot 60°- Cos 45°?

A) (9 - 2√3)/9 B) (2√6 - 1)/√3 C) (1 - 2√3)/2 D) (√2 - √3)/√6

Answer 1

cot 60° - cos 45° = (√2 - √3)/√6

Given :

The expression cot 60° - cos 45°

To find :

The value of cot 60° - cos 45° is

A) (9 - 2√3)/9

B) (2√6 - 1)/√3

C) (1 - 2√3)/2

D) (√2 - √3)/√6

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is cot 60° - cos 45°

Step 2 of 2 :

Find the value of the expression

cot 60° - cos 45°

$\displaystyle \sf{ = \frac{1}{ \sqrt{3} } - \frac{1}{ \sqrt{2} } }$

[ LCM of the denominators = √6 ]

$\displaystyle \sf{ = \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{ 6} } }$

Hence the correct option is D) (√2 - √3)/√6

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