Correct Answer - Option 3 : 0
As per trigonometric properties
tan θ = cot (90 - θ) and tan θ . cot θ = 1
thus, tan 89° = cot (90 -89° ) = cot 1°
similarly, tan 88° = cot 2°, tan 87° = cot 3° ans so on...
also from Logarith properties
log m +log n = log (m × n)
thus, log tan 1° + log tan 89° = log (tan1° × tan89°)
= log (tan1° × cot1°)
= log 1
= 0
similarly, log tan 2° + log tan 88° = log (tan1° × cot1°) = log 1 = 0
thus, log tan1° +log tan2° +……..+log tan 89° = 0.
