How do you simplify #Sin (x+(pi/6)) - sin (x-(pi/6)) #?
1 Answer
Feb 21, 2016
cosx
Explanation:
Using
#color(blue)" Addition Formulae"# sin(A ± B ) = sinAcosB ± cosAsinB
(1)
#sin(x+pi/6 ) = sinxcos(pi/6 )+ cosxsin(pi/6)# (2)
#sin(x - pi/6 ) = sinxcos(pi/6) - cosxsin(pi/6)# Placing expansions from (1) and (2) back into original expression.
#sinxcos(pi/6) +cosxsin(pi/6) - [sinxcos(pi/6) - cosxsin(pi/6)]# now
#sinxcos(pi/6) - sinxcos(pi/6) = 0# and
#cosxsin(pi/6) + cosxsin(pi/6) = 2cosxsin(pi/6)#
#rArr2cosxsin(pi/6) = 2cosx xx 1/2 = cosx#