Question 1125840
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(1) {{{sin(pi/5) = sin((2*(pi/10))) = 2sin(pi/10)cos(pi/10)}}}<br>
(2) {{{cos(pi/10) = sqrt(1-sin(pi/10)^2)}}}<br>
Substitute (2) into (1)  and use the given value of sin(pi/10) to get<br>
{{{sin(pi/5) = 2((-1+sqrt(5))/4)*sqrt(1-((-1+sqrt(5))/4)^2)}}}
 = {{{((-1+sqrt(5))/2)*sqrt(1-(6-2*sqrt(5))/16)}}}
 = {{{((-1+sqrt(5))/2)*(sqrt(10+2*sqrt(5))/4)}}}
 = {{{((-1+sqrt(5))*sqrt(10+2*sqrt(5)))/8}}}<br>
Evaluating sin(pi/5) and that expression on a scientific calculator gives identical results, confirming the correctness of the expression.