Question

sin36º sin 72° sin 108° sin 144° is equal to
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Answer 1

Answer:

Step-by-step explanation:

=sin 36 * sin 72 * sin 108 * sin 144

= sin 36 * sin 72 * sin (180 – 72) * sin(180 – 36)

we know that sin (180 – θ) = sinθ

= sin 36 * sin 72 * sin 72 * sin 36

= [sin 36 * sin 72]²

=¼ [ 2 sin 36 * sin 72]²

formula 2sin(A)*sin(B) = [cos(A-B) – cos(A+B)]  

=¼ [ cos 36 – cos 108]²

cos(108) = cos(90+18) = -sin(18)

=¼ [ cos 36 + sin 18]²

put cos 36 = (√5 + 1)/4 and sin 18 = (√5 – 1)/4  

=¼ [ (√5 + 1)/4 + (√5 – 1)/4]² ;

=¼ [ √5/2 ]²

= 5/16  answer…