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ivann1987 [24]
3 years ago
7

Find cos 18, sin 18. cos 3x=sin2x then x=18.

Mathematics
1 answer:
Rzqust [24]3 years ago
6 0
X = 18°
cos 54° = sin 36°
cos 3 x = sin 2 x
cos ( 2 x + x ) = sin 2 x
cos 2 x cos x - sin 2 x sin x = 2 sin x cos x
( cos² x - sin² x ) cos x - 2 sin² x cos x = 2 sin x cos x   / : cos x
                                                                         ( divide both sides by cos x )
cos² x - sin² x - 2 sin² x = 2 sin x
1 - sin² x - 3 sin² x - 2 sin x = 0
- 4 sin² x - 2 sin x + 1 = 0               substitution:  u = sin x
- 4 u² - 2 u + 1 = 0
u = 2 -√20 / - 4        sin 18° =  (√ 5 - 1 )/4 
sin 18 =  \frac{ \sqrt{5} -1 }{4}
cos 18° = √( 1² - ((√5 - 1)/4)²
cos 18° = (10+2√5)^(1/2) / 4

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