sin18-

sin18-

Question Number 197908 by mathlove last updated on 03/Oct/23

s i n 18^{°} = ?

Answered by universe last updated on 03/Oct/23

\sin (36 ° + 54 °) = \sin 90 °

36 ° + 54 ° = 90 °

x = 18 °

5 x = 2 x + 3 x = 90 °

2 x = 90 ° - 3 x

\sin 2 x = \sin (90 ° - 3 x)

\sin 2 x = \cos 3 x

2 \sin x \cos x = {4 \cos}^{3} x - 3 \cos x

2 \sin x = {4 \cos}^{2} x - 3

2 \sin x = 4 - {4 \sin}^{2} x - 3

{4 \sin}^{2} x + 2 \sin x - 1 = 0

\sin x = \frac{- 2 \pm 2 \sqrt{5}}{8}

\sin x = \frac{- 1 \pm \sqrt{5}}{4}

\sin 18 ° = \frac{\sqrt{5} - 1}{4}

Commented by mathlove last updated on 03/Oct/23

t h a n k s