Log 10tan 1-log 10tan 2-log 10tan 89-

The correct option is A 0log_10[tan1^∘.tan2^∘… tan44^∘ tan45^∘ tan46^∘… tan89^∘] =log_10[(tan1^∘.tan89^∘)… tan 45^∘] =log_10[(tan1^∘.cot1^∘)… tan 45^∘] =log_10 ...

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Byju's Answer

Standard IX

Mathematics

Fundamental Laws of Logarithms

log 10tan 1∘+...

Question

$l o g_{10} t a n 1^{\circ} + l o g_{10} t a n 2^{\circ} + \dots l o g_{10} t a n 89^{\circ}$

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Solution

$l o g_{10} [t a n 1^{\circ} . t a n 2^{\circ} \dots t a n 44^{\circ} t a n 45^{\circ} t a n 46^{\circ} \dots t a n 89^{\circ}]$
$= l o g_{10} [(t a n 1^{\circ} . t a n 89^{\circ}) \dots t a n 45^{\circ}]$
$= l o g_{10} [(t a n 1^{\circ} . c o t 1^{\circ}) \dots t a n 45^{\circ}]$
$= l o g_{10} 1 = 0$ $[∵ t a n 1^{\circ} . c o t 1^{\circ} = 1]$

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Similar questions

Q. Solve

l o g_{10} t a n 1^{\circ} + l o g_{10} t a n 2^{\circ} + . . . . . . . . + l o g_{10} t a n 89^{\circ}

Q. The value of

{log}_{10} tan 1^{\circ} + {log}_{10} tan 2^{\circ} + {log}_{10} tan 3^{\circ} . . . . + {log}_{10} tan 89^{\circ}

Find the value of the sum

{log}_{10} tan 1^{\circ} + {log}_{10} tan 2^{\circ} + . . . . {log}_{10} tan 89^{\circ}

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log10 tan1∘+log10 tan2∘+…log10 tan 89∘

log10[tan1∘.tan2∘…tan44∘tan45∘tan46∘…tan89∘] =log10[(tan1∘.tan89∘)…tan45∘] =log10[(tan1∘.cot1∘)…tan45∘] =log10 1=0 [∵tan1∘.cot1∘=1]

$l o g_{10} t a n 1^{\circ} + l o g_{10} t a n 2^{\circ} + \dots l o g_{10} t a n 89^{\circ}$