How do you simplify #cos (x+pi/6)+sin(x-pi/3)#?
1 Answer
Feb 2, 2016
0
Explanation:
Using the following trigonometric identities :
#• cos (A + B ) = cosAcosB - sinAsinB .........(1) #
#• sin (A - B ) = sinAcosB - cosAsinB ...........(2)# Applying these to the question :
from(1) :
# cos(x + pi/6 ) = cosxcos(pi/6) - sinxsin(pi/6)# and using exact values:
# =cosx .sqrt3/2 - sinx . 1/2 .......(a)# from (2) :
# sin(x-pi/3 ) = sinxcos(pi/3) - cosxsin(pi/3)# using exact values :
# = sinx1/2 - cosx.sqrt3/2........(b) # combining (a) and (b)
# sqrt3/2 cosx - 1/2 sinx + 1/2 sinx - sqrt3/2 cosx = 0#
