The value of tan1∘×tan2∘×tan3∘×…...×tan89∘ is :
0
1
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∘)] . [(tan2∘. tan(90∘−2∘)]..........[(tan44∘.tan(90∘−44∘)].1
=(tan1∘. cot1∘). (tan2∘. cot2∘) ....... (tan44∘. cot44∘)
=1