11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[\frac{x}{\cos \theta }=\frac{y}{\cos \left( \theta -\frac{2\pi }{3} \right)}=\frac{z}{\cos \left( \theta +\frac{2\pi }{3} \right)},\]then \[x+y+z=\]

    A) \[1\]

    B) \[0\]

    C) \[-1\]

    D) None of these

    Correct Answer: B

    Solution :

    We have \[\frac{x}{\cos \theta }=\frac{y}{\cos \left( \theta -\frac{2\pi }{3} \right)}=\frac{z}{\cos \left( \theta +\frac{2\pi }{3} \right)}=k\] Þ \[x=k\cos \theta \], \[y=k\cos \left( \theta -\frac{2\pi }{3} \right)\], \[z=k\cos \left( \theta +\frac{2\pi }{3} \right)\] Þ \[x+y+z=k\left[ \cos \theta +\cos \left( \theta -\frac{2\pi }{3} \right)+\cos \left( \theta +\frac{2\pi }{3} \right) \right]\] \[=k[(0)=0\] \[\Rightarrow \] \[x+y+z=0\].


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