perplexus.info :: Just Math : Logtan Expression Quickie

Logtan Expression Quickie (Posted on 2023-08-28)

Using only p&p, determine the value of this expression:

log(tan 1^o)+log(tan 2^o)+log(tan 3^o)+...............+log(tan 88^o)+log(tan 89^o)

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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Solution (Spoiler)

| Comment 1 of 3

It sums to 0.

log(tan 1^o) =

log(sin 1^o/cos 1^o) = log(sin 1^o/sin 89^o) = log(sin 1^o)- log(sin 89^o)

log(tan 89^o) =

log(sin 89^o/cos 89^o) = log(sin 89^o/sin 1^o) = log(sin 89^o)- log(sin 81^o)

These two terms sum to 0

All terms cancel out except log(tan 45^o) = log(1) = 0

So, the sum is 0

Posted by Steve Herman on 2023-08-28 09:09:19

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