Solving \frac 58 \cot 36^{\circ}=\cos^3 x without substituting the trig

Kaspaueru2 2022-01-16 Answered
Solving 58cot36=cos3x without substituting the trig values for 36
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otoplilp1
Answered 2022-01-17 Author has 41 answers
Since
cos3x=3cosx+cos3x4
we need to prove that:
5cos368sin36=3cos18+cos544
or
5cos36=3sin54+3sin18+sin90sin18
or
2cos36+2cos108=1
which is true because
2cos36+2cos108=2sin36cos36+2sin36cos108sin36=
=sin72+sin144sin72sin36=1
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Jordan Mitchell
Answered 2022-01-18 Author has 31 answers
58cot36=5cos368sin36=5cos2364cos18 Using Proving trigonometric equation cos(36)cos(72)=12 cos36(2cos2361)=125cos236=(1+cos36)2=(2cos218)2
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