State whether the following statement is true or false:
$c o s e c 20^{\circ} sec 20^{\circ} =$

2

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2 c o s e c 40^{\circ}

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4

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2 sin 45^{\circ} . c o s e c 40^{\circ}

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Solution

The correct option is B $2 c o s e c 40^{\circ}$
$c s c 20 sec 20$

$⟹ \frac{1}{sin 20 cos 20}$

$⟹ \frac{2}{2 sin 20 cos 20}$

$⟹ \frac{2}{sin 2 (20)}$

$⟹ \frac{2}{sin 40}$

$⟹ 2 csc 40$

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