How to prove that #2sin((4pi)/5)cos(pi/5)=sin((2pi)/5)#?
2 Answers
May 28, 2018
Using
we obtain
and finally
May 28, 2018
Explanation:
#"using the "color(blue)"product to sum formula"#
#•color(white)(x)2sinxcosy=sin(x+y)+sin(x-y)#
#"here "x=(4pi)/5" and "y=pi/5#
#"consider left side"#
#sin((4pi)/5+pi/5)+sin((4pi)/5-pi/5)#
#=sinpi+sin((3pi)/5)#
#=0+sin(pi-(3pi)/5)#
#=sin((2pi)/5)=" right side"rArr" verified"#