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Verify the identity cot theta + fraction {sin theta}{1 + cos theta} = csc theta.

Question:

Verify the identity {eq}\displaystyle cot \ \theta + \frac {sin \ \theta}{1 + cos \ \theta} = csc \ \theta. {/eq}

Trigonometric Identities

The object of verifying a trigonometric identity is to demonstrate that the left side and the right side of it are exactly the same.

Usually, some transformations are needed in one or both sides to achieve that. We must use the basic trigonometric identities, which include:

{eq}\displaystyle \cos^2 x +\sin^2 x =1 \\ \sec^2 x - \tan^2 x =1 \\ \displaystyle \frac{1}{\sin x} =\csc x , \frac{1}{\cos x} =\sec x \\ \displaystyle \frac{\sin x}{\cos x} =\tan x , \frac{\cos x}{ \sin x} =\cot x {/eq}

The sine of an angle in a right angles triangle can be defined as the ratio of the opposite side to the hypotenuse.

The cosine of an angle in a right angles triangle can be defined as the ratio of the adjacent side to the hypotenuse.

Answer and Explanation: 1

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Let {eq}\displaystyle I =\cot \theta +\frac{\sin \theta}{1+ \cos \theta} {/eq}

Multiply and divide {eq}\displaystyle 1- \cos \theta {/eq} to...

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Trigonometric Identities: Definition & Uses

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Chapter 23 / Lesson 1
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Trigonometric identities are equations that are always true for trigonometric functions. Learn about the definition and kinds of trigonometric identities and explore the uses of trigonometric identities through examples.


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