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Domain and Range of Trigonometric Ratios

What is sin A...

Question

What is sin A cos A tan A + cos A sin A cot A equal to ?

sin A

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cos A

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tan A

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Solution

The correct option is D 1
$sin A . cos A . tan A + cos A . sin A . cot A$
$= sin A . cos A (tan A + cot A)$
$= sin A . cos A (tan A + \frac{1}{tan A})$
$= sin A . cos A . (\frac{{tan}^{2} A + 1}{tan A}) = sin A cos A \frac{{sec}^{2} A}{tan A}$
$= 1$

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