Chapter: Trigonometry· Mathematics Part 2 (Geometry)
Answer: Proved.
\(\sec\theta - \cos\theta = \dfrac{1}{\cos\theta} - \cos\theta = \dfrac{1 - \cos^2\theta}{\cos\theta} = \dfrac{\sin^2\theta}{\cos\theta}\)
\(\cot\theta + \tan\theta = \dfrac{\cos^2\theta + \sin^2\theta}{\sin\theta\cos\theta} = \dfrac{1}{\sin\theta\cos\theta}\)
LHS \(= \dfrac{\sin^2\theta}{\cos\theta} \times \dfrac{1}{\sin\theta\cos\theta} = \dfrac{\sin\theta}{\cos^2\theta} = \dfrac{\sin\theta}{\cos\theta} \times \dfrac{1}{\cos\theta} = \tan\theta\,\sec\theta\) = RHS.