2sin15cos45 ? Evaluate

1 Answer
Jim G.
Apr 14, 2018

#1/2(sqrt3-1)#

Explanation:

#"using the "color(blue)"trigonometric identities"#

#•color(white)(x)sin(x+-y)=sinxcosy+-cosxsiny#

#"note that "#

#sin(x+y)+sin(x-y)#

#=sinxcosycancel(+cosxsiny)+sinxcosycancel(-cosxsiny)#

#=2sinxcosy#

#"here "x=15" and " y=45#

#rArr2sin15cos45=sin(15+45)+sin(15-45)#

#color(white)(xxxxxxxxxxxx)=sin60+sin(-30)#

#color(white)(xxxxxxxxxxxx)=sin60-sin30#

#color(white)(xxxxxxxxxxxx)=sqrt3/2-1/2=1/2(sqrt3-1)#

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