সমাধান করুন: \(\frac{{\sin \theta }}{{1 + cos\theta }} + \frac{{1 + cos\theta }}{{sin\theta }} = ?\) A. tan θ B. cot θ C. \(\frac{2}{{sin{\rm{\theta }}}}\) D. \(\frac{2}{{cos{\rm{\theta }}}}\)

উত্তর দেখান ও ব্যাখ্যা

উত্তর: (D) C

ব্যাখ্যা

Over a common denominator: [sin²θ + (1 + cosθ)²] / [sinθ(1 + cosθ)] = [sin²θ + cos²θ + 1 + 2cosθ] / [sinθ(1 + cosθ)] = (2 + 2cosθ) / [sinθ(1 + cosθ)] = 2(1 + cosθ) / [sinθ(1 + cosθ)] = 2/sinθ.