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JEE Main & Advanced Mathematics Straight Line Question Bank Angle between two straight lines, Bisector of angle between two lines

  • question_answer
    The angle between the lines \[x\cos {{30}^{o}}+y\sin 30{}^\circ =3\] and \[x\cos {{60}^{o}}+y\sin {{60}^{o}}=5\] is

    A)            \[{{90}^{o}}\]                      

    B)            \[{{30}^{o}}\]

    C)            \[{{60}^{o}}\]                      

    D) None of these

    Correct Answer: B

    Solution :

               \[\theta ={{\tan }^{-1}}\left( \frac{-\cot {{30}^{o}}+\cot {{60}^{o}}}{1+\cot {{30}^{o}}\cot {{60}^{o}}} \right)\]                       \[={{\tan }^{-1}}\left( \frac{\tan {{60}^{o}}-\tan {{30}^{o}}}{1+\tan {{30}^{o}}\tan {{60}^{o}}} \right)={{30}^{o}}\].


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