Question

Find the value of sin18 degree and sin 54 degree

Answer 1

Answer:

Step-by-step explanation:

sin$54^{0}$ =sin($90^{0} -36^{0}$)=cos$36^{0}$=$\frac{\sqrt{5}+1 }{4}$

sin$18^{0}$=

let Θ(teta)=$18^{0}$

5teta= $90^{0}$

2teta+3teta=$90^{0}$

2teta=$90^{0}$-3teta

sin2teta=sin($90^{0}$-3teta)=cos3teta

2sinteta.costeta=4$cos^{3}$teta-3costeta

costeta(2sinteta-4$cos^{2}$teta+3)=0

2sinteta-4(1-$sin^{2}$teta)+3=0

2sinteta+4$sin^{2}$teta-1=0

let sinteta=x then

4$x^{2}$+2x-1=0

x=$\frac{-b+or-\sqrt{b^{2}-4ac } }{2a}$   (substitute b=2,a=4,c=-1 in these formula)

x=$\frac{-1+or-\sqrt{5} }{4}$

sinteta=$\frac{-1+or-\sqrt{5} }{4}$