Question

Find the value of log(tan 1)+ log(tan2)+....+log(tan89):

Answer 1

Step-by-step explanation:

Log (tan 1)+ Log(tan2)+......+ Log(tan 89)

= 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