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# Trigonometry Question for Explanation

The Image shows all the Details.., The correct option is B.., I want to know B is the answer

Note by Vamsi Krishna Appili
3 years, 6 months ago

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Notice that \begin{align*} n = \sec \theta + \csc \theta &= \frac{1}{\cos \theta} + \frac{1}{\sin \theta} \\ &= \frac{\sin \theta + \cos \theta}{\sin \theta \cos \theta} \\ &= \frac{m}{\sin \theta \cos \theta}. \end{align*} Also, if we square the first given equation, we find that $m^2 = \sin^2 \theta + \cos^2 \theta + 2 \sin \theta \cos \theta \\ m^2 - 1 = 2 \sin \theta \cos \theta \\ \frac{m^2 - 1}{2} = \sin \theta \cos \theta.$ Therefore, $n = \frac{2m}{m^2 - 1} \\ 2m = n(m^2 - 1)$ and the answer is B. · 3 years, 6 months ago