Question

log tan1 + log tan 2 + log tan3 ........ logtan 89

Answer 1

 Log (tan(1)* tan(2) * .. * tan(89)) 
all the angles are in degrees... 

but tan(k°) = cot(90° - k°) ... property of cofunctions... 

thus 
we have 
Log( tan(1)* tan(2)*...* tan(44)* tan(45)*...* tan(88)* tan(89)) 

= Log( tan(1)* tan(2)*...* tan(44)* cot(44)*...* cot(2)* cot(1)) 

= Log(1) 

= 0