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JEE Main & Advanced Sample Paper JEE Main Sample Paper-18

  • question_answer
    If in an isosceles triangle with base \[a,\] vertical angle of \[20{}^\circ \] and lateral side each of length \[b\] are given then value of\[{{a}^{3}}+{{b}^{3}}\]equals

    A)  \[3ab\]                               

    B)  \[3a{{b}^{2}}\]

    C)  \[3{{a}^{2}}b\]                

    D)  \[3\]

    Correct Answer: B

    Solution :

     \[\sin 10{}^\circ =\frac{a}{2b}\] \[\Rightarrow \] \[\sin 30{}^\circ =3\,\sin 10{}^\circ -4\,{{\sin }^{3}}10\] \[\Rightarrow \] \[\frac{1}{2}=\frac{3a}{2b}-\frac{4{{a}^{3}}}{8{{b}^{3}}}\] \[\Rightarrow \] \[{{a}^{3}}+{{b}^{3}}=3\,a{{b}^{2}}\]


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