A) 1 |
B) 0 |
C) -1 |
D) None |
A) 1 |
\( tan \left(90 ^{\circ} - \theta \right) = cot \theta \)
\( tan 89 ^{\circ} = tan \left(90 ^{\circ} -1\right) = cot 1 ^{\circ} \)
Therefore, \( tan1 ^{\circ} . tan2 ^{\circ} . tan3 ^{\circ} .........tan87 ^{\circ} . tan88 ^{\circ} . tan89 ^{\circ} \)
= \( tan1 ^{\circ} . tan2 ^{\circ} . tan3 ^{\circ} ..... tan45 ^{\circ} ..... cot3 ^{\circ} . cot2 ^{\circ} . cot1 ^{\circ} \)
=\( \left(tan1 ^{\circ} .cot1 ^{\circ} \right) \left(tan2 ^{\circ} .cot2 ^{\circ} \right) \left(tan3 ^{\circ} . cot3 ^{\circ}\right) ..... \left(tan45 ^{\circ} \right) \)
= \( 1 \times 1 \times 1 .... \times 1 = 1 \)