Find the value of $tan 20^{o} + 2 tan 50^{o}$

tan 40

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tan 60

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tan 70

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tan 80

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Solution

The correct option is C $tan 70$

$t a n 20^{\circ} + 2 t a n 50^{\circ} = t a n 20^{\circ} + t a n 50^{\circ} + t a n 50^{\circ}$

$= t a n 70^{\circ} (1 - t a n 20^{\circ} t a n 50^{\circ}) + t a n 50^{\circ}$ $(t a n (20 + 50)^{\circ} = \frac{t a n 20^{\circ} + t a n 50^{\circ}}{1 - t a n 20^{\circ} t a n 50^{\circ}})$

$= t a n 70^{\circ} - t a n 20^{\circ} t a n 50^{\circ} t a n 70^{\circ} + t a n 50^{\circ}$

$= t a n 70^{\circ} - c o t 70^{\circ} t a n 50^{\circ} t a n 70^{\circ} + t a n 50^{\circ}$

$= t a n 70^{\circ} - \frac{1}{t a n 70^{\circ}} \times t a n 50^{\circ} t a n 70^{\circ} + t a n 50^{\circ}$

$= t a n 70^{\circ} - t a n 50^{\circ} + t a n 50^{\circ}$

$= t a n 70^{\circ}$

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tan 10^{\circ} tan 20^{\circ} tan 30^{\circ} tan 40^{\circ} tan 50^{\circ} tan 60^{\circ} tan 70^{\circ} tan 80^{\circ}

tan 40^{\circ} + tan 60^{\circ} + tan 80^{\circ} = tan 40^{\circ} . tan 60^{\circ} . tan 80^{\circ}

Find the value of: tan 20^o. tan 40^o. tan 50^o. tan 60^o. tan 70^o

tan 20^{\circ} . tan 40^{\circ} . tan 60^{\circ} . tan 80^{\circ} = k

k

tan 20^{\circ} tan 40^{\circ} tan 80^{\circ} = tan 60^{\circ}

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