Solve $(\frac{\sqrt{3}}{cos (2 A)}) - (\frac{1}{sin (2 A)}) = 4$ $(sqrt(3)/cos(2A))-(1/sin(2A))=4$ ?

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Solve $(\frac{\sqrt{3}}{cos (2 A)}) - (\frac{1}{sin (2 A)}) = 4$ $(sqrt(3)/cos(2A))-(1/sin(2A))=4$ ?

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Answer 1 · 2017-10-20T12:06:05

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Explanation:

$\frac{\sqrt{3}}{cos 2 A} - \frac{1}{sin 2 A} = 4$ $sqrt3/(cos2A)-1/(sin2A)=4$
$\Rightarrow \sqrt{3} \cdot sin 2 A - cos 2 A = 4 \cdot sin 2 A \cdot cos 2 A$ $=>sqrt3 cdot sin2A-cos2A=4 cdot sin2A cdot cos2A$
$\Rightarrow \frac{\sqrt{3}}{2} \cdot sin 2 A - \frac{1}{2} cos 2 A = 2 \cdot sin 2 A \cdot cos 2 A$ $=>sqrt3/2 cdot sin2A-1/2cos2A=2 cdot sin2A cdot cos2A$
$\Rightarrow sin 2 A \cdot {cos 30}^{\circ} - cos 2 A \cdot {sin 30}^{\circ} = sin 4 A$ $=>sin2A cdot cos30^@-cos2A cdot sin30^@=sin4A$
$\Rightarrow sin (2 A - 30^{\circ}) = sin 4 A$ $=>sin(2A-30^@)=sin4A$
$\Rightarrow 2 A - 30^{\circ} = 4 A$ $=>2A-30^@=4A$
$\Rightarrow 2 A = - 30^{\circ}$ $=>2A=-30^@$
$\Rightarrow A = - 15^{\circ}$ $=>A=-15^@$

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Solve $(\frac{\sqrt{3}}{cos (2 A)}) - (\frac{1}{sin (2 A)}) = 4$ $(sqrt(3)/cos(2A))-(1/sin(2A))=4$ ?

1 Answer

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