How do you prove this: cos(x+30) + sinx = cos (x-30) ???

Question

its an identity. Ive been tryin 4 ages but I cant find a way??? any help please??

Answer 1

Try this.
cos(30)= sqrt(3)/2
cos(a+b)=cos(a)cos(b)-sin(a)sin(b)
a=x b=30
cos(a-b)=cos(a)cos(b)+sin(a)sin(b)
and prove the identity.

Answer 2

LHS
cos x cos 30 - sin x sin 30 + sin x
√3/2 cos x - (1/2) sin x + sin x
√3/2 cos x + (1/2) sin x

RHS
cos x cos 30 + sin x sin 30
(√3/2) cos x + (1/2) sin x

LHS = RHS

Answer 3

cos(x+30) + sinx = cos (x-30)
cosxcos30 - sinxsin30 +sinx = cos xcos30 +sinxsin30
(-sinx) (.5) +sinx = .5sin x
sinx = .5sinx +.5sinx = sinx