How do you determine the values of the given function?

Question

#sin 105 degrees# by using # 105=60+45#

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Answer 1 · 2018-02-19T10:54:37

See below.

Identity:

#color(red)bb(sin(A+B)=sinAcosB+cosAsinB)#

#sin(105)=sin(60+45)->#

#=sin60cos45+cos60sin45#

#:.#

#sin60=sqrt(3)/2# #color(white)(888888)sin45=sqrt(2)/2#

#cos60=1/2# #color(white)(88888888)cos45=sqrt(2)/2#

#:.#

#sqrt(3)/2*sqrt(2)/2+1/2*sqrt(2)/2#

#sqrt(6)/4+sqrt(2)/4=(sqrt(6)+sqrt(2))/4~~0.9659# ( 4 .d.p.)