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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Mock Test - Trigonometric Functions

  • question_answer
    If \[y=(1+tan\,A)(1-tan\,B),\]where A-B=\[\frac{\pi }{4}\], then \[{{(y+1)}^{y+1}}\]is equal to

    A) 9                     

    B) 4

    C) 27                    

    D) 81

    Correct Answer: C

    Solution :

    [c] \[A-B=\frac{\pi }{4}\] or tan (A-B)= \[\tan \frac{\pi }{4}\] Or \[\frac{\tan A-\tan B}{1+\tan A\tan B}=1\] Or \[\tan A-\tan B-\tan A\tan B=1\] Or \[\tan A-\tan B-\tan A\tan B+1=2\] Or \[(1+tanA)(1-tanB)=2\Rightarrow y=2\] Hence, \[{{(y+1)}^{y+1}}={{(2+1)}^{2+1}}={{(3)}^{3}}=27\]


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