Question

Trying to solve an identity with the sum and difference formula, (working one side):
sin (pi/6) + x)) + sin (pi / 6) -x)) = cos x

Answer 1

so we can start expanding out the formula we get ...

sin(pi/6)cos(x) + sin(x)cos(pi/6) + sin(pi/6)cos(x) - cos(pi/6)sin(x)
so now we get two terms because the other two terms cancel out. the term that cancels out is sin(x)cos(pi/6) so we simplify to

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

so ... 2sin(pi/6)cos(x)

now we know that sin(pi/6) = 1/2
so 2* ( 1/2) =1
hence

1*cos(x) = cos(x)

Answer 2

Thank you so much! I really appreciate your expertise! :)

Answer 3

np :)

Answer 4

:)