How do you simplify #sin(x + (3π)/2) cos x#?
2 Answers
Sep 10, 2016
Explanation:
knowing that
knowing that
Sep 10, 2016
Explanation:
Expand
#sin(x+(3pi)/2)" using "color(blue)"addition formula"#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(sin(A+B)=sinAcosB+cosAsinB)color(white)(a/a)|)))#
#rArrsin(x+(3pi)/2)=sinxcos((3pi)/2)+cosxsin((3pi)/2)#
#color(orange)"Reminder"#
#color(red)(bar(ul(|color(white)(a/a)color(black)(cos((3pi)/2)=0" and " sin((3pi)/2)=-1)color(white)(a/a)|)))#
#rArrsinxcos((3pi)/2)+cosxsin((3pi)/2)#
#=0-cosx=-cosx#
#rArrsin(x+(3pi)/2)cosx=-cosx(cosx)=-cos^2x#