JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Solution of trigonometrical equations

  • question_answer
    If \[(1+\tan \theta )(1+\tan \varphi )=2\], then \[\theta +\varphi \]= [Karnataka CET 1993]

    A) \[{{30}^{o}}\]

    B) \[{{45}^{o}}\]

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

    D) \[{{75}^{o}}\]

    Correct Answer: B

    Solution :

    \[(1+\tan \theta )\,\,(1+\tan \varphi )=2\Rightarrow \frac{\tan \theta +\tan \varphi }{1-\tan \theta \tan \varphi }=1\] \[\Rightarrow \]  \[\tan (\theta +\varphi )=1\] \[\Rightarrow \] \[\theta +\varphi =\frac{\pi }{4}\] = 45o.


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