In a ∆ABC if sides a and b remain constant such that a is the error in C, then relative error in its area, is

# In a $∆ABC$ if sides a and b remain constant such that $a$ is the error in $C,$ then relative error in its area, is

1. A

$\alpha \mathrm{cot}C$

2. B

$\alpha \mathrm{sin}C$

3. C

$\alpha \mathrm{tan}C$

4. D

$\alpha \mathrm{cos}C$

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### Solution:

We have,

$S=\frac{1}{2}ab\mathrm{sin}C⇒\frac{dS}{dC}=\frac{1}{2}ab\mathrm{cos}C$

Let $∆S$ be the error in area $S.$ Then,

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