Question

Review the steps in the derivation of the tangent sum identity. The steps are not in order.

A 2-column table with 4 rows. Column 1 has entries 1, 2, 3, 4. Column 2 has entries StartFraction sine (x + y) Over cosine (x + y) EndFraction, StartStartFraction StartFraction sine (x) cosine (y) Over cosine (x) cosine (y) EndFraction + StartFraction cosine (x) sine (y) Over cosine (x) cosine (y) EndFraction OverOver StartFraction cosine (x) cosine (y) Over cosine (x) cosine (y) EndFraction minus StartFraction sine (x) sine (y) Over cosine (x) cosine (y) EndFraction EndEndFraction, StartFraction tangent (x) + tangent (y) Over 1 minus tangent (x) tangent (y) EndFraction, StartFraction sine (X) cosine (y) + cosine (x) sine (y) Over cosine (x) cosine (y) minus sine (x) sine (y) EndFraction.

Which list shows the steps in the correct order?

I --> II --> IV --> III
I --> IV --> II --> III
III --> I --> II --> IV
III --> I --> IV --> II

Answer 1

Answer:

The answer is B: I  IV II  III

Step-by-step explanation:

Just did it

Answer 2

The sequence for the derivation of tangent sum identity is option I --> IV --> II --> III.

What is trigonometric identity?

The trigonometric identities is the relationship between the different trigonometric ratios. These trigonometric identities are the basic formulae that are true for all the values of the reference angle.

For the given situation,

The derivation for the tangent sum identity is given in the table below.

The derivation follows the steps,

$\frac{sin(x+y)}{cos(x+y)}$

we know that, $sin(x+y) = sinx cosy + cosx siny$ ,

$cos(x+y)=cosxcoxy - sinxsiny$ and

$\frac{sinx}{cosx}=tanx$

⇒ $\frac{sinxcosy + cosxsiny}{cosxcosy-sinxsiny}$

Divide each term by $cosxcosy$

⇒ $\frac{\frac{sinxcosy}{cosxcosy} +\frac{cosxsiny }{cosxcosy} }{\frac{cosxcosy}{cosxcosy} -\frac{sinxsiny}{cosxcosy} }$

⇒ $\frac{tanx+tany}{1-tanxtany}$

Hence we can conclude that the derivation of tangent sum identity is option I --> IV --> II --> III.

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