If ( )=f(x)-g(x)+c, then:

MCQ

If $\int\sin\text{xd}(\sec\text{x})=\text{f}(\text{x})-\text{g}(\text{x})+\text{c},$ then:

A
$\text{f}(\text{x})=\sec\text{x}$
✓
$\text{f}(\text{x})=\tan\text{x}$
C
$\text{g}(\text{x})=2\text{x}$
D
$\text{g}=-\text{x}$

✓

Answer

Correct option: B.

$\text{f}(\text{x})=\tan\text{x}$

$\int\sin \text{xd}(\sec\text{x})=\int\sin\text{x}\sec\text{x}\tan\text{xdx}$
$=\int\tan^2\text{xdx}$
$=\int(\sec^2\text{x - 1})\text{dx}$
$=\tan\text{x - x}+\text{c}$
$\Rightarrow\text{f}(\text{x})=\tan\text{x},\text{g}(\text{x})=\text{x}$

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