tanθcotθ=1,
tan (90−θ) =cotθ
and tan45°=1
Given: tan1°.tan2°,tan3° …….tan88°. tan89°
= (tan1°. tan89°),(tan2°. tan88°)…..(tan44°.tan46°) (tan45°)
= [(tan1°. tan (90°−1°)]. [(tan 2°. tan(90°−2°)]………. [(tan44°. tan(90°−44°)].1
= (tan1°. cot1°). (tan2°. cot2°) ……. (tan44°. cot44°)
= 1