Question

How do you simplify `cos (x+pi/6)+sin(x-pi/3)`?

Answer 1

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`