Determine whether the following equations/identities are true:

$$\sin(75^\circ)=\sin(105^\circ)$$

$$\tan(220^\circ)=\tan(40^\circ)$$
 $$\cos(350^\circ)=\cos(170^\circ)$$
Development:

An angle of $$75^\circ$$ and one of $$105 ^\circ$$ are supplementary, since $$75^\circ+105 ^\circ=180^\circ$$. Since the sines of supplementary angles are equal, the identity is true.

An angle of $$220^\circ$$ and one of $$40^\circ$$ differ in $$180^\circ$$, because $$220^\circ40^\circ=180^\circ$$. Since the angles that differ in $$180^\circ$$ have the same tangent, then the equation is false.
 An angle of $$350^\circ$$ and one of $$170^\circ$$ differ in $$180^\circ$$, since $$350^\circ170^\circ =180^\circ $$. The cosines of angles that differ in $$180^\circ$$ have equal cosines, but with a different sign. That is: $$\cos(350^\circ)=\cos(170^\circ)$$, therefore the identity is true.
Solution:
 The identity is true.
 The identity is false.
 The identity is true.