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  • Need clarity, kindly explain! - Considering only the principal values of inverse functions, the set - Trigonometry - JEE Main

Considering only the principal values of inverse functions, the set A=\left \{ x\geq 0:\tan ^{-1}(2x)+\tan ^{-1}(3x)=\frac{\pi }{4} \right \}

  • Option 1)

     

    is a singleton 

  • Option 2)

     

    contains two elements

  • Option 3)

     

    contains more than two elements

  • Option 4)

     

    is an empty set 

Answers (1)

best_answer

 

Addition Formulae -

\tan \left ( A+B \right )= \frac{\tan A+\tan B}{1-\tan A\tan B}

- wherein

A and B are two angles.

\tan^{-1}2x+\tan^{-1}3x=\frac{\pi}{4}

Taking tan both sides we get,

\frac{2x+3x}{1-6x^{2}}=1

6x^{2}+5x-1=0

=>(x+1)(6x-1)=0

=>x=\frac{1}{6}   ( -1 is rejected)

 


Option 1)

 

is a singleton 

Option 2)

 

contains two elements

Option 3)

 

contains more than two elements

Option 4)

 

is an empty set 

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