Question 824157
How to solve it:
4 sin 5Pi/12 cos 5pi/12 = ?
Answers:
a ) √ 2
b) 1
c) √ 3
d) - 1
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Identities:(half-angle formulas for sin and cos)
{{{sin(5pi/12)=sin(5pi/6)/2=sqrt((1-cos(5pi/6))/2)=sqrt((1-(-sqrt(3)/2))/2)=sqrt(((1+sqrt(3)/2))/2))=sqrt(2+sqrt(3)/4))}}}=√(2+√3)/2
..
{{{cos(5pi/12)=cos(5pi/6)/2=sqrt((1+cos(5pi/6))/2)=sqrt((1+(-sqrt(3)/2))/2)=sqrt(((1-sqrt(3)/2))/2))=sqrt(2-sqrt(3)/4))}}}=√(2-√3)/2
..
4 sin 5Pi/12 cos 5pi/12 = 4*√(2+√3)/2*√(2-√3)/2=4*√(4-3)/4=4*1/4=1

ans: b)  1