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If theta=pi/(4n) then the value of tanth...

If `theta=pi/(4n)` then the value of `tanthetatan(2theta)tan(3theta)....tan((2n-1)theta)` is

Text Solution

Verified by Experts

The correct Answer is:
1
`2n theta=pi//2`
`:. theta,(2n-1)theta=(pi//2)-theta`
`or 2theta,(2n-2)theta=(pi//2)-2theta,...`
They form complementary angles A and B so that `tanA tanB=tanAcotA=1` for each pair.
Also, `tanntheta=tan. Pi/4=1`
Hence, the value of product is 1
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