If in a triangle `A B C` , the side `c` and the angle `C` remain constant, while the remaining elements are changed slightly, using differentials show that `(d a)/(c sA)+(d b)/(cosB)=0`

Explanation

In a triangle, we have

By sine Formula,`a/(sinA)=b/(sinB)=c/(sinC)`

Given that side c and angle C is constant

=`c/(sinC)=K`(assume)

`a/(sinA)=b/(sinB)=K`

Or,`a=KsinA,b=KsinB`

Differentiating a and b, we have

`(da)/(cosA)=KdA`

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