prove that Sin^6 ϴ-cos^6ϴ=(2Sin^2ϴ-1)(cos^2ϴ+sin^4ϴ) please sove step by step with language it is opt maths question ​ ​

Elaborate on the reason(s) that matter is said to move even as in a solid state. select one: a. the particles are bound through intermolecular forces but are able to move past each other with relative freedom. b. the particles have sufficient energy to become an ionized gas and are in the most common state of matter in the universe. c. the particles are not able to move out of their positions relative to one another, but do have small vibrational movements. d. the particles are not bound to one another, move quickly, have a low density, and are able to spread apart from one another if unconstrained.