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If in a triangle `A B C ,`the side `c`and the angle `C`remain constant, while the remaining elements are changed slightly,show that`(d a)/(cosA)+(d b)/(cosB)=0.` |
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Answer» As given , we have `(c)/(sinC) = k` (constant) `:. (a)/(sin A) = (b)/(sin B) = k rArr a = k sin A and b = k sin B` `:. da = k cos A .dA and db = k cos B. dB` or `(da)/(cos A) + (db)/(cos B) = k (dA + dB) = kd (A + B) = kd (pi - C) = 0` Hence, `(da)/(cos A) + (db)/(cos B) = 0` |
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