Double angle identities Problems and Solutions

In trigonometry, the double angle identities are used as formulas while solving the trigonometric problems and here is the list of trigonometry problems with answers and step by step solution for understanding how to use double angle identities in various trigonometry questions.

Evaluate $\dfrac{1}{\sin{10^\circ}}-\dfrac{\sqrt{3}}{\cos{10^\circ}}$

Evaluate $\dfrac{-\sin{x}+\sin{2x}}{1-\cos{x}+\cos{2x}}$