List of top Mathematics Questions on Trigonometric Identities asked in HPBOSE Class XII

Find the values of the other five trigonometric functions, if \( \cos x = -\frac{1}{2} \), and \( x \) lies in the third quadrant.
Prove that \( \frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x - y}{2} \).