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

Note by Vamsi Krishna Appili 4 years, 1 month ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

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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.

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B

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Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestNotice 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.

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B

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