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