In a ` Delta` ABC if sides a and b remain constant such that a is the error in C, thenrelatinv error in its area, is

Options

A. `a cot C `
B. a sin C
C. a tan C
D. a cos C

Answer

A

Explanation

We have,
`S=1/2ab" "sin C rArr (dS)/(dC)= 1/2 ab" "cos C`
Let `Delta S` be the error in area S. Then, `DeltaS=(dS)/(dC)Delta C`
`rArr" "DeltaS=1/2ab" "cos C" "a " "[:' DeltaC = a]`
`(DeltaS)/S=(1/2ab cosC)/(1/2ab sin C)a = a cot C`