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 ​ ​

In a laboratory experiment, a fermenting aqueous solution of glucose and yeast produces carbon dioxide gas and ethanol. the solution was heated by burning natural gas in a bunsen burner to distill the ethanol that formed in the flask. during the distillation, the ethanol evaporated and then condensed in the receiving flask. the flame of the burner was kept too close to the bottom of the flask and some of the glucose decomposed into a black carbon deposit on the inside of the flask. during this experiment the following changes occurred. which of these changes involved a physical change and not a chemical change? check all that apply. 1-condensation of ethanol 2-evaporation of ethanol 3- formation of carbon dioxide gas from glucose burning of natural gas 4-formation of ethanol from glucose by yeast 5-formation of a carbon deposit inside the flask

What happens when the temperature of a solution increases?

When water dissociates, each water molecule splits into a hydroxide ion and a) h 3 o + b) a hydrogen atom c) a hydrogen ion d) h 2 o e) oh —