Question

The value of 2tan23°×tan35°×tan30°×tan67°is___

Answer 1

Answer:

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given :2tan 23° × tan 35° × tan 30° × tan 67° is

We know that

$( \tan(90) - 0) = \cot(0)$

therefore,

$2 \tan(90 - 67) \times \tan(90 - 55) \times \tan(30) \times \tan(55) \times \tan(67)$

$2 \cot(67) \times \cot(55) \times \tan(30) \times \tan(55) \times \tan(67)$

also,

$\tan(0) = \frac{1}{ \cot(0) }$

thus,

$2 \cot(67) \times \cot(55) \times \tan(30) \tan(55) \times \tan(67)$

$2 \times \frac{1}{ \tan(67) } \times \frac{1}{ \tan(65) } \times \tan(30) \times \tan(55) \times \tan(67)$

$2 \tan(30)$

$2 \times \frac{1}{ \sqrt{3} }$

$= \frac{2}{ \sqrt{3} } answer$

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