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Range of Trigonometric Ratios from 0 to 90 Degrees

If 2A-3= 0,...

Question

If ${cot}^{2} A - 3 = 0$ , find the value of $sin 2 A$ .

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Solution

$c o t^{2} A = 3$
$c o t A = \sqrt{3}$
$c o t A = c o t 30$
$A = 30^{\circ}$
Now, $s i n 2 A = s i n 60 = \frac{\sqrt{3}}{2}$

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