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

  • question_answer
    The number of solution of equation \[6\cos 2\theta +2{{\cos }^{2}}(\theta /2)+2si{{n}^{2}}\theta =0,\]\[-\pi <\theta <\pi \]is

    A) 3                     

    B) 4

    C) 5                     

    D) 6

    Correct Answer: A

    Solution :

    [a] \[6\cos 2\theta +2{{\cos }^{2}}(\theta /2)2si{{n}^{2}}\theta =0\] Or \[12{{\cos }^{2}}\theta -6+1+\cos \theta +2-2{{\cos }^{2}}\theta =0\] or \[10{{\cos }^{2}}\theta +\cos gq-3=0\] or \[(5cos\theta +3)(2cos\theta -1)=0\] or \[\cos \theta =-\frac{3}{5},\frac{1}{2}\] \[\Rightarrow \theta =\frac{\pi }{3};\pi -{{\cos }^{-1}}\left( \frac{3}{5} \right),-\frac{\pi }{3},-\pi +{{\cos }^{-1}}\left( \frac{3}{5} \right)\]


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