Explanation of Working Model of Trignometry Functions Formulas.

Reciprocal Identities: 

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Introduction:- This working model helps to learn all the trigonometry ratio and function formulas. You can make this working model by watching this video.

Explanation - 

Quotient and Reciprocal Identities

When it comes to more advanced studies in trigonometry, eventually using just sine, cosine, and tangent on their own won't be enough. That is why it is so important to learn about what we call "quotient" and "reciprocal" identities.

That being said, before we get into using these quotient and reciprocal identities, it is crucial that you have a thorough understanding of how to use Sine, Cosine, and tangent.

Reciprocal Identities
sinθ = 1/cosecθ
cosecθ = 1/sinθ
cosθ = 1/secθ
secθ = 1/cosθ
tanθ = 1/cotθ
cotθ = 1/tanθ

Quotient Identities

In trigonometry, quotient identities refer to trig identities that are divided by each other. There are two quotient identities that are crucial for solving problems dealing with trigs, those being for tangent and cotangent. Cotangent, if you're unfamiliar with it, is the inverse or reciprocal identity of the tangent. This identity will be more clear in the next section. Below, this image covers the two fundamental identities you must know when it comes to quotient identities.

Reciprocal Identities

Have you ever wondered if there was an easier way of dealing with trigonometric expressions such as $\sin ^{-1} x$? It turns out, there is. In trigonometry, reciprocal identities or inverse identities cover this base. Instead of writing $\sin ^{-1} x$ or $1/ \sin x$ , we can use the reciprocal identity cosec x instead. Cosecant (csc), secant (sec), and cotangent (cot) are extremely useful identities, and you will use them extensively as you progress with mathematics into pre-calculus and calculus. Therefore, it is quintessential that you memorize and understand all of these identities. The image below covers what you must know.

Using Quotient and Reciprocal Identities

Now that we've covered what quotient and reciprocal identities are, let's get into how to use them. As always, the best way to learn and get comfortable with these identities is to do some practice problems.

Example 1:

Simplify the expression:

$$\frac{\cos x \cdot \tan x + \sin x}{2\tan x}