prove that: -1/4 cos36 cos18 = -1/4 cot18

Answer 1

-1/4 cos36 cos18 = -1/4 cot18
then prove:
cos36 cos18 = cot18

we know cos 2A = 2cos^2 A - 1
cos36 = 2cos^2 18 - 1

LS = cos36cos18
= (2cos^2 18 - 1)(cos18)
= 2cos^3 18 - cos18

RS = 1/tan18

Not even remotely true, check your typing

Btw, 18° and 36° are part of the group of the "golden ratio" associated angles, that is, 18°, 36°, 72°, 108°
Their trig ratios can all be expressed as exact values,
e.g.
cos 36° = (√5 + 1)/4, which is half of the golden ratio
sin 18° = (√5 - 1)/4 , which is half of the decimal part of the golden ratio
cos 108° = (1-√5)/4 , which is the negative of half the decimal of the GR
etc