The value of log $$tan$$ $$1$$∘$$+log$$⁡$$tan$$⁡$$2$$∘$$+$$…$$+log$$⁡$$tan$$⁡$$89$$∘ is

log⁡$$tan$$⁡$$1$$∘$$+log$$⁡$$tan$$⁡$$2$$∘$$+$$…$$+log$$⁡$$tan$$⁡$$89$$∘$$=log$$⁡$$1=0$$

Trigonometric equations

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Question

The value of log tan $1^{\circ} + \log \tan 2^{\circ} + \dots + \log \tan 89^{\circ}$ is

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Solution

$\log \tan 1^{\circ} + \log \tan 2^{\circ} + \dots + \log \tan 89^{\circ} = \log 1 = 0$

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