Question

Prove the identity \( \sec^2 \theta = 1 + \tan^2 \theta \) for any right-angled triangle and use it to show that: \[ \frac{\sin \theta - \cos \theta + 1}{\sin \theta + \cos \theta - 1} = \frac{1}{\sec \theta - \tan \theta}. \]

Hint:

Using identities like \( \sec^2 \theta = 1 + \tan^2 \theta \) can simplify complex trigonometric expressions.

Answer 1