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Sign of Trigonometric Ratios in Different Quadrants

Solve: 12o. ...

Question

Solve:
$cot 12^{o} . cot 38^{o} . cot 52^{o} . cot 60^{o} . cot 78^{o}$

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Solution

$cot 12 ° \cdot cot 38 ° \cdot cot 52 ° \cdot cot 60 ° \cdot cot 78 °$
$= (cot 12 ° \cdot cot 78 °) \cdot (cot 38 ° \cdot cot 52 °) \cdot cot 60 °$
$= (cot 12 ° \cdot cot (90 ° - 12 °)) \cdot (cot 38 ° \cdot cot (90 ° - 38 °)) \cdot cot 60 °$
$= (cot 12 ° \cdot tan 12 °) \cdot (cot 38 ° \cdot tan 38 °) \cdot cot 60 °$
$= 1 \times 1 \times \frac{1}{\sqrt{3}}$
$= \frac{1}{\sqrt{3}}$

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