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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer
    If \[x=\sin {{130}^{o}}\,\cos {{80}^{o}},\,\,y=\sin \,{{80}^{o}}\,\cos \,{{130}^{o}},\,\,z=1+xy,\]which one of the following is true [AMU 1999]

    A) \[x>0,\,\,y>0,\,\,z>0\]

    B) \[x>0,\,\,y<0,\,\,0<z<1\]

    C) \[x>0,\,\,y<0,\,\,z>1\]

    D) \[x<0,\,\,y<0,\,0<z<1\]

    Correct Answer: B

    Solution :

    \[x=\sin {{130}^{o}}\cos {{80}^{o}},\] \[y=\sin {{80}^{o}}\cos {{130}^{o}}\] Þ \[x=\cos {{40}^{o}}\cos {{80}^{o}},\,\,\,y=-\sin {{80}^{o}}\sin {{40}^{o}}\] So, \[x>0\] and \[y<0and\]\[xy<0\] Now\[z=1+xy\] Þ \[0<z<1\]. 


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