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Kumar Gaurav

· started a discussion

· 1 Months ago

confusion (Question: 186294.0 )

How tan1tan89=1?

Question:
Find the value of tan 1º and 2º tan 3º...........tan 89º. 
Options:
A) 1
B) 0
C) \(\sqrt{3}\)
D) \(\cfrac{1}{\sqrt{3}}\)
Solution:
Ans: (a)


Knowledge Expert

· commented

· 1 Months ago

tan1.tan2.........tan89
tan 89 can be written as cot 1[tan(90-1)=cot 1] by tan(90-theta)=cot(theta)
likewise......,
tan 88 =cot 2
tan 87= cot 3
................up to tan 46=cot 44
then middle one is tan 45 =1
so it is
tan1.tan2...........tan44.tan 45.cot44..............cot1
tan and cot cancel out by[tan (theta)*cot(theta)=1
so ....remaining is 1
answer =1
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