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Step-by-step explanation:
y=logtan1°+logtan2°+…..+logtan45°+logtan46°+…..+logtan89°
y=logtan1°+logtan2°+……+logtan45°+logcot(90°-46°)+…….+logcot(90°-89°)
y=logtan1°+logtan2°+………logtan44°+ log(1) + logcot44°+………+logcot1°
From property of logarithm we have
loga+logb+logc=log(abc)
y=log(tan1°.tan2°.tan3°……tan44°.1.cot44°…….cot1°)
We know from trigonometric functions
Tanx.cotx=1
So cancelling the consecutive terms in the above equation we get
y=log(1.1.1.. …1)
y=log(1)
y=0
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