11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[\tan \,(A+B)=p,\,\,\tan \,(A-B)=q,\] then the value of \[\tan \,2A\] in terms of p and q is [MP PET 1995, 2002]

    A) \[\frac{p+q}{p-q}\]

    B) \[\frac{p-q}{1+pq}\]

    C) \[\frac{p+q}{1-pq}\]

    D) \[\frac{1+pq}{1-p}\]

    Correct Answer: C

    Solution :

    \[2A=(A+B)+(A-B)\] \[\Rightarrow \]\[\tan 2A=\frac{\tan (A+B)+\tan (A-B)}{1-\tan (A+B)\tan (A-B)}=\frac{p+q}{1-pq}\].

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