The value of tan1°tan2° tan3°....... tan89° is : tan 1° tan 2° tan 3° ...... tan 89°

tan1°.tan2°.tan3°... tan45°... tan88°tan89°

= (tan1°.tan89°) (tan2°. tan88°) ... tan45°

= (tan1°.cot1°).(tan2°.cot2°) ... tan45° = 1

$left[ecause an left(90^{circ}- heta ight)=cot heta, an heta cdot cot heta=1 ight]$