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A is an angle in the fourth quadrant. If satisfies the trigonometric equation $3\left(3-\tan ^{2} \mathrm{~A}-\cot \mathrm{A}\right)^{2}=1$.
Which one of the following is a value of A?
Options:
Which one of the following is a value of A?
Solution:
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Verified Answer
The correct answer is:
$300^{\circ}$
Checking through options $300^{\circ}=-60^{\circ}$
So, $3\left[3-\tan ^{2}\left(-60^{\circ}\right)-\cot \left(-60^{\circ}\right)\right]^{2}$
$=3\left[3-3+\frac{1}{\sqrt{3}}\right]^{2}=3 \times \frac{1}{3}=1$
So, $3\left[3-\tan ^{2}\left(-60^{\circ}\right)-\cot \left(-60^{\circ}\right)\right]^{2}$
$=3\left[3-3+\frac{1}{\sqrt{3}}\right]^{2}=3 \times \frac{1}{3}=1$
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