Sine

$$ \sin (x±y)= \sin x\cos y±\cos x \sin y $$

sin implies flip sin and cos of x and y for the next cos and sin

sin first, then sin last.

Cosine

$$ \cos (x±y) = \cos x\cos y ∓\sin x\sin y $$

cos implies cos with cos, sin with sin. flip only the add and subtraction sign

Tangent

$$ \tan (x±y) =\frac {\tan x±\tan y} {1∓\tan x\tan y} $$

tan implies two term of tan of x and y , follow sign on top.

two term of 1 and tan x with tan y, oppose sign on underneath.

<aside> 💡 sin(x)+sin(y) not equals to sin(x+y)

</aside>

So When Encounter with Theta of non 30,45,60 Multiple

You can use those identities to solve for those thetas.