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10th Class Mathematics Introduction to Trigonometry Question Bank Trigonometry

  • question_answer
    If in a \[\Delta ABC\] m \[\angle A=\frac{\pi }{2}\], then value of \[{{\cos }^{2}}\,A+{{\cos }^{2}}B+{{\cos }^{2}}C\] is

    A) 3

    B) 2

    C) \[\frac{3}{2}\]

    D) 1

    Correct Answer: D

    Solution :

     In \[\Delta \,ABC,\]   \[A+B+C=\pi \] or            \[\frac{\pi }{2}+B+C=\pi \] or            \[B+C=\frac{\pi }{2}\] or            \[C=\frac{\pi }{2}-B\] \[\therefore \]  \[{{\cos }^{2}}A+{{\cos }^{2}}B+{{\cos }^{2}}C\]                 \[={{\cos }^{2}}\frac{\pi }{2}+{{\cos }^{2}}B+{{\cos }^{2}}\left( \frac{\pi }{2}-B \right)\]                 \[=0+({{\cos }^{2}}B+{{\sin }^{2}}B)=1\]


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