Chapter: Trigonometry· Mathematics Part 2 (Geometry)
Answer: Proved.
Multiply numerator and denominator inside the root by \((1 - \sin\theta)\):
LHS \(= \sqrt{\dfrac{(1 - \sin\theta)^2}{(1 + \sin\theta)(1 - \sin\theta)}} = \sqrt{\dfrac{(1 - \sin\theta)^2}{1 - \sin^2\theta}} = \sqrt{\dfrac{(1 - \sin\theta)^2}{\cos^2\theta}}\)
\(= \dfrac{1 - \sin\theta}{\cos\theta}\) (for acute θ both are positive)
\(= \dfrac{1}{\cos\theta} - \dfrac{\sin\theta}{\cos\theta} = \sec\theta - \tan\theta\) = RHS.