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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If \[\tan A-\tan B=x\] and \[\cot B-\cot A=y\], then the value of \[\cot (A-B)\] is

    A) \[x-y\]

    B) \[x+y\]

    C) \[\frac{1}{x}-\frac{1}{y}\]

    D) \[\frac{1}{x}+\frac{1}{y}\]

    Correct Answer: D

    Solution :

     \[\cot \,B-\cot \,A=y\] or            \[\frac{\tan \,A-\tan B}{\tan A\,\tan B}=y\] or            \[\tan A\,\tan \,B=\frac{x}{y}\] Now,     \[\cot \,(A-B)=\frac{1}{\tan \,(A-B)}\] \[=\frac{1+\tan A\,\tan B}{\tan A-\tan B}\] \[=\frac{1+\frac{x}{y}}{x}=\frac{1}{x}+\frac{1}{y}\]


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