see attachment and explain with solution

Hello student,
We know that in a triangle, by Sine rule,
a/sin A = b/sin B = c/sin C
Given that c and C are constants
So, we have c/sin C = k (say)
therefore, a/sin A = b/sin B = k.
This gives a = k sin A and b = k sin B.
da = k cos A dA
db = k cos b dB
So, da/cos A + db/cos B = k dA + k dB
= k (dA + dB)
= k d(A + B)
= k d(π – C)
= 0.
Hence, da/cos A + db/cos B = 0.