The value of tan $1^{\circ}$ $\times$ tan $2^{\circ}$ $\times$ tan $3^{\circ}$ $\times$ …... $\times$ tan $89^{\circ}$ is :

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Solution

The correct option is B
1

$tan θ cot θ = 1,$

$tan (90 - θ) = c o t θ$

and $t a n 45^{\circ} = 1$

Given: $t a n 1^{\circ}$ . $t a n 2^{\circ}$ , $t a n 3^{\circ}$ ....... $t a n 88^{\circ}$ . $t a n 89^{\circ}$

= ( $t a n 1^{\circ}$ . $t a n 89^{\circ}$ ),( $t a n 2^{\circ}$ . $t a n 88^{\circ}$ ).....( $t a n 44^{\circ}$ . $t a n 46^{\circ}$ ) ( $t a n 45^{\circ}$ )

= [( $t a n 1^{\circ}$ . $t a n (90^{\circ} - 1^{\circ}$ )] . [( $t a n 2^{\circ}$ . $t a n (90^{\circ} - 2^{\circ}$ )]..........[( $t a n 44^{\circ}$ . $t a n (90^{\circ} - 44^{\circ}$ )].1

= ( $t a n 1^{\circ}$ . $c o t 1^{\circ}$ ). ( $t a n 2^{\circ}$ . $c o t 2^{\circ}$ ) ....... ( $t a n 44^{\circ}$ . $c o t 44^{\circ}$ )

= 1

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Similar questions

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . . . tan 89^{\circ}

tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} \dots tan 89^{\circ}

The value of $tan 1^{\circ} tan 2^{\circ} tan 3^{\circ} . . . . . . tan 89^{\circ}$ is

t a n 1^{\circ} . t a n 2^{\circ} . t a n 3^{\circ} . . . . . . . . . . t a n 89^{\circ}

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