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In `Delta ABC`, the side c and angle C are constant. If there are small changes in the remaining sides and angles, then show that `(da)/(cos A) +(db)/(cos B)= 0`. |
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Answer» We know that `a/(sin A) = b/(sin B) = c/(sin C)` But c and C are constant. Therefore `a/(sin A)= b/(sin B) = k` ` rArr a=k sin A and b=k sin B` ` rArr (da)/(dA) = k cos A and (db)/(dB) k cos B` `rArr (da)/(cos A) = k * dA and (db)/(cos B) = k * dB` `rArr (da)/(cos A) + (db)/(cos B) = k(dA+ dB)` ` = k d (A+B) - k d (pi - C)` ` = k * (0)` `=0` ` :. (da)/(cos A) + (db)/(cos B) = 0`. |
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