Trigonometry Question for Explanation

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

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

Notice that $\begin{aligned} n = \sec \theta + \csc \theta &= \frac{1}{\cos \theta} + \frac{1}{\sin \theta} \\ &= \frac{\sin \theta + \cos \theta}{\sin \theta \cos \theta} \\ &= \frac{m}{\sin \theta \cos \theta}. \end{aligned}$ 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.

Josh Petrin - 7 years, 9 months ago

melad jalali - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$