logtan1° + logtan2° +....+ log tan89°
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= Log (tan(1)* tan(2) * .. * tan(89))
all the angles are in degrees...
but tan(k°) = cot(90° - k°) ... property of cofunctions...
thus
we have
Log( tan(1)* tan(2)*...* tan(44)* tan(45)*...* tan(88)* tan(89))
= Log( tan(1)* tan(2)*...* tan(44)* cot(44)*...* cot(2)* cot(1))
= Log(1)
= 0
= Log (tan(1)* tan(2) * .. * tan(89))
all the angles are in degrees...
but tan(k°) = cot(90° - k°) ... property of cofunctions...
thus
we have
Log( tan(1)* tan(2)*...* tan(44)* tan(45)*...* tan(88)* tan(89))
= Log( tan(1)* tan(2)*...* tan(44)* cot(44)*...* cot(2)* cot(1))
= Log(1)
= 0
Soundaryasarvade:
Prove it..I need the solution with steps plz
done ok?
Thanks a lot
if it helped you pls mark as brainliest
Ok
Answered by
0
Answer:
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Step-by-step explanation:
Log[tan1°×tan2°×......... ×tan89°]
log[ tan1°×tan2°×.......... cot2°×cot1°]
After getting cancelled
log(tan45°)
Tan45°=1
Log1°=0
I HOPE THIS MAY HELP YOU
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