Question 1205806



{{{sin (105)}}}°={{{sin (60+45)}}}°


Use the addition identity 


{{{sin(alpha +beta)=sin(alpha)cos(beta)+cos(alpha)sin(beta)}}}


{{{sin (105)}}}°={{{sin(60)cos(45)+cos(60)sin(45)}}}


{{{sin (105)}}}°={{{(sqrt(3)/2)(1/sqrt(2))+(1/2)(1/sqrt(2))}}}


{{{sin (105)}}}°={{{sqrt(3)/(2sqrt(2))+1/(2sqrt(2))}}}.....rationalize

{{{sin (105)}}}°={{{(sqrt(3)sqrt(2))/(2sqrt(2)*sqrt(2))+sqrt(2)/(2sqrt(2)*sqrt(2))}}}


{{{sin (105)}}}°={{{sqrt(6)/4+sqrt(2)/4}}}


{{{sin (105)}}}°={{{(sqrt(6)+sqrt(2))/4}}}