The value of (tan1° tan2° tan3° ... tan89°) is

0.0

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0.5

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Solution

The correct option is C 1
(tan1° tan2° tan3° ... tan89°)

This can be written as,

(tan1° tan2° tan3° ....... tan44° tan45° tan46° ..... tan87° tan88° tan89°)

= [tan1° tan2° tan3° ....... tan44° tan45° tan (90 – 44)° ..... tan(90° - 3) tan (90° - 2) tan (90° - 1)]

= (tan1° tan2° tan3° ....... tan44° tan45° cot 44° ..... cot3° cot2° cot 1°)

= 1

(Since tan and cot are reciprocals of each other, they cancel each other.)

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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 $1^{\circ}$ $\times$ tan $2^{\circ}$ $\times$ tan $3^{\circ}$ $\times$ …... $\times$ 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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