InterviewSolution
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InterviewSolution
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In the ambiguous case if the remaining angles of a triangle with given a, b, A and `B_(1),B_(2),C_(1),C_(2)` then `(sin C_(1))/(sin B_(1))+(sin C_(2))/(sin B_(2))=`A. 2 cos AB. 2 sin BC. 2 tan AD. 2 cot A |
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Answer» Correct Answer - A `a^(2)=b^(2)+c^(2)-2bc` coa A or `c^(2)-(2b cos A)c+b^(2)-a^(2)=0` Above equation has two roots `c_(1)` and `c_(2)` `therefore c_(1)+c_(2)=2bcos A` and `c_(1)c_(2)=b^(2)-a^(2)` `sin B_(1)=sin B_(2)=(b sin A)/(a)` `sin C_(1)=(c_(1)sin A)/(a)` `sin C_(2)=(c_(2)sin A)/(a)` `therefore (sin C_(1))/(sin B_(1))+(sin C_(2))/(sin B_(2))=(c_(1)+c_(2))/(b)=2 cos A` |
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