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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simple solution

Comment 3 of 3 |

log(a)+log(b)=log(ab) So we can find the product of the arguments first.

tangents of complementary angles are reciprocals. So most of these pairs have a product of 1. The only angle left is 45, but tan(45)=1.

So we have log(1) = 0.

Posted by Jer on 2023-08-28 10:29:52

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