The Value of logtan10+logtan20+⋯⋯+logtan890 is
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0
It should be at last logtan89
log ( tan 10 tan 20.........tan 89)
As tan 10 tan 89 tan 20 tan 88......tan45)
tan 10 tan ( 90 -10) tan20 tan ( 90 -20)......tan 45
tan 10 cot 10 tan20 cot20...........1
1
So log 1
0
So 0 is the answer
log ( tan 10 tan 20.........tan 89)
As tan 10 tan 89 tan 20 tan 88......tan45)
tan 10 tan ( 90 -10) tan20 tan ( 90 -20)......tan 45
tan 10 cot 10 tan20 cot20...........1
1
So log 1
0
So 0 is the answer
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