Question

find the value of x cosec 3x = (cot 30° + cot 60°) / (1 + cot 30° cot 60° cot 30°)

Answer 1

The value of x = 60°

Given:

cosec 3x = (cot 30° + cot 60°) / (1 + cot 30° cot 60°)

In given problem the denominator might be wrong the corrected one is

(1 + cot 30° cot 60°)

To find:

The value of x

Solution

Given cosec 3x = (cot 30° + cot 60°) / (1 + cot 30° cot 60° )

As we know from trigonometric table

cot 30° = √3 and cot 60° = 1/√3

Take RHS from given problem

RHS = (cot 30° + cot 60°) / (1 + cot 30° cot 60° )

substitute cot 30° = √3 and cot 60° = 1/√3 value

= $\frac{\sqrt{3} + \frac{1}{\sqrt{3} } }{1 + \sqrt{3}(\frac{1}{\sqrt{3} } ) }$

= $\frac{\sqrt{3} + \frac{1}{\sqrt{3} } }{1 + 1 }$  

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

=  $\frac{3 +1}{\sqrt{3} } (\frac{1}{2})$

=  $\frac{4}{\sqrt{3} } (\frac{1}{2}) = \frac{2}{\sqrt{3} }$

cosec 3x = 2/√3

As we know cosec 60° = 2/√3  

⇒ cosec 3x = cosec 60°

⇒ 3x = 60°

⇒ x = 20°

The value of x = 60°

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