KVPY Sample Paper KVPY Stream-SX Model Paper-27

  • question_answer
    The expression, \[\frac{(a+b+c)\,\,(b+c-a)\,\,(c+a-b)\,\,(a+b-c)}{4{{b}^{2}}{{c}^{2}}}\]equal to-

    A) \[{{\cos }^{2}}A\]

    B) \[si{{n}^{2}}A\]

    C) \[cos\,\,A\,\,\cos \,\,A\,\,\cos \,\,C\]

    D) none of these

    Correct Answer: B

    Solution :

    \[\frac{2s\,\,(2s-2a)\,\,(2s-2b)\,\,(2s-2c)}{4{{b}^{2}}{{c}^{2}}}\]\[=\frac{16\,\,(s)\,\,(s-a)\,\,(s-b)\,\,(s-c)}{4{{b}^{2}}{{c}^{2}}}=\frac{4{{\Delta }^{2}}}{{{b}^{2}}{{c}^{2}}}\]
    \[\frac{4\times {{\left[ \frac{1}{2}bc.\sin A \right]}^{2}}}{{{b}^{2}}{{c}^{2}}}={{\sin }^{2}}A\]


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