Write the value of tan $10^{o}$ tan $20^{o}$ tan $70^{o}$ tan $80^{o}$ .

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Solution

tan $10^{o}$ tan $20^{o}$ tan $70^{o}$ tan $80^{o}$

$= t a n 10 t a n 20 c o t (90 - 70) c o t (90 - 80)$

$= t a n 10 t a n 20 c o t 20 c o t 10$

as we know $t a n Q \times c o t Q = 1$
so
$t a n 10 c o t 10 t a n 20 c o t 20 = 1$

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