Multiple angle identities Problems and solutions

Double angle identities

$(1).\,\,$ Evaluate $\dfrac{1}{\sin{10^\circ}}-\dfrac{\sqrt{3}}{\cos{10^\circ}}$

$(2).\,\,$ Find $\dfrac{-\sin{x}+\sin{2x}}{1-\cos{x}+\cos{2x}}$

Triple angle identities

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

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