We know that
sin18∘=45−1
cosec18∘=sin18∘1=5−14
Rationalizing denominator
=5−14×5+15+1
=44(5+1)
=5+1
Hence equation x=5+1
⇒(x−1)2=5
⇒x2−2x+1=5
⇒x2−2x−4=0
cosec18∘ is a root of the equation:
Held on 31 Aug 2021 · Verified 6 Jul 2026.
x2−2x−4=0
4x2+2x−1=0
x2+2x−4=0
x2−2x+4=0
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