Solve

Sin 36 Sin 72 Sin 108 Sin 144 = ?
Please solve this...

=>sin36°sin72°sin108°sin144°
=>(Sin36×sin72)²
=>1/4 (2sin36×sin72)²
=>1/4(cos(-36)+cos108)²
=>1/4 {cos36+sin18}² ........eq1

Now,
Let x=18°
5x=90°
2x+3x=90
2x=90-3x
Sin2x=sin(90-3x)
2sinx cosx =cos3x
2sinx cosx = 4cos³x-3cosx
2sinx=4cos²x-3
4sin²x+2sinx-1=0
(ax²+bx+c=0)
Sinx=-2±√20/8
Sin18°=√5-1/4 ........(2)

Cos36=cos2×18x
Cos2x=cos²x-sin²x

Similarly,
Cos36=√5+1/4 .....(3)

Put 2 and 3 in eq 1 we get
1/4{√5+1 +√5-1/4}²
1/4 × 5/4
5/16

Solve it

21600/45 = 480

480 = 2^5 * 3 * 5


No. of co-prime pairs of factors =

(a + 1)(b + 1)(c + 1) + ab + bc + ca + 3abc - 1

49

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