Question

Please slove it log×tan1+log×tan2+.......+log×tan89=?

Answer 1

Answer:

0

Step-by-step explanation:

Given :

To find the value of :

log (tan 1°) + log (tan 2°) + log (tan 3°) + ...+ log(tan 45°) ... + log (tan 89°)

Solution :

We know that,

log (tan 89°) = log(cot 1°) = log(1/tan1°) = -log(tan 1°)

log (tan 88°) = log(cot 2°) = log(1/tan2°) = -log(tan 2°)

log (tan 87°) = log(cot 3°) = log(1/tan3°) = -log(tan 3°)

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∴

⇒ log (tan 1°) + log (tan 2°) + log (tan 3°) + ...+ log(tan 45°) ... + log (tan 89°)

⇒ log (tan 1°) + log (tan 2°) + log (tan 3°) + ...+ log(tan 45°) ... - log (tan 3°) - log (tan 2°) - log (tan 1°)

⇒ [log(tan 1°) - log(tan 1°)] + [log(tan 2°) - log(tan 2°)] + [log(tan 3°) - log(tan 3°)] + .... log(tan 45°)

⇒ 0 + log(tan 45°) = 0 + log(1) = 0 + 0 = 0