Help with TRIGONOMENTRY

[mainstein]

I need to write these simpler but i have no idea how.

a) cos (x+pi/3) + sin(x+pi/6)

b) sin(x)/sin(x+pi/6)-sin(x-pi/6)

PLEASE help, I'm grateful.

 

[stapel]

I need to write these simpler but i have no idea how.

How is "simpler" defined?

a) cos (x+pi/3) + sin(x+pi/6)

What did you get when you applied angle-sum identities to each of the two trig expressions (including evaluating at the known angle values)?

b) sin(x)/sin(x+pi/6)-sin(x-pi/6)

Is just the "sin(x + pi/6)" in the denominator, or is the difference of the two sine expressions all underneath the initial sine? Either way, what did you get when you applied angle-sum and -difference identities, etc?

Please be complete. Thank you!