Question : Which of the following is equal to $\sec A – \cos A$?
Option 1: $\sin A\cot A$
Option 2: $\cot A\ cos A$
Option 3: $\tan A\sin A$
Option 4: $\cos A\sin A$
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Correct Answer: $\tan A\sin A$
Solution :
Given: The trigonometric expression is $\sec A – \cos A$.
We know the trigonometric identity $1–\cos^2 A= \sin^2 A$.
⇒ $\sec A – \cos A$
$=\frac{1}{\cos A}–\cos A$
$=\frac{1–\cos^2 A}{\cos A}$
$=\frac{\sin^2 A}{\cos A}$
$=\frac{\sin A}{\cos A}\times \sin A=\tan A\sin A$
Hence, the correct answer is $\tan A\sin A$.
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