Question

If 3sinA + 2cosA = 0 tyen the value of cot2A is equal to:

a. -4/3
b. -12/5
c. -5/12
d. -3/4

Answer 1

c) -5/12 is answer ok...

Answer 2

Answer:

$cot2A=-\frac{5}{12}$

Step-by-step explanation:

Given: $3sinA+2cosA=0$.

To find value of $cot2A$.

Dividing both sides by $sinA$ in given equation we have;

$3+2cotA=0\\cotA=-\frac{3}{2}$

Now using formula, $cot2x=\frac{cot^{2}x-1 }{2cotx}$ we have;

$cot2A=\frac{(-\frac{3}{2} )^{2}-1 }{2(\frac{-3}{2}) }$

         $=\frac{\frac{9}{4} -1}{-3}\\=-\frac{5}{12}$

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