Triple angle identities Questions with solutions

The list of trigonometry questions on triple angle identities for practice with understandable solutions to learn how to use the triple angle trigonometric identities as formulas in math problems. The triple angle trigonometric problems were solved here in different methods to enhance problem-solving skill in you. So, learn each method to get solution for any type of trigonometric question with triple angle identities.

$(1).\,\,$ Find $\dfrac{\sin{3x}}{\sin{x}}$ $-$ $\dfrac{\cos{3x}}{\cos{x}}$

$(2).\,\,$ Evaluate $\dfrac{\cos{x}-\cos{3x}}{\cos{x}}$ $+$ $\dfrac{\sin{x}+\sin{3x}}{\sin{x}}$

$(3).\,\,$ Calculate $\dfrac{\cos^3{x}-\cos{3x}}{\cos{x}}$ $+$ $\dfrac{\sin^3{x}+\sin{3x}}{\sin{x}}$

$(4).\,\,$ Find $(\sin{3x}+\sin{x})\sin{x}$ $+$ $(\cos{3x}-\cos{x})\cos{x}$