Question

Read the proof.

A 2-column table with 3 rows. Column 1 is labeled Step with entries tangent (2 x) = tangent (x + x), question mark, = StartFraction 2 (x) Over 1 minus tangent squared (x) EndFraction. Column 2 is labeled Reason with entries Addition, question mark, simplify.

What is the missing step and reason?

Equals StartFraction tangent (x) + tangent (x) Over 1 minus tangent (x) tangent (x) EndFraction tangent double angle identity
Equals StartFraction tangent (x) + tangent (x) Over 1 minus tangent (x) tangent (x) EndFraction tangent sum identity
Equals StartFraction tangent (x) + tangent (x) Over 1 + tangent (x) tangent (x) EndFraction tangent double angle identity
Equals StartFraction tangent (x) + tangent (x) Over 1 + tangent (x) tangent (x) EndFraction tangent sum identity

Answer 1

Answer:

Its B kiddos

Step-by-step explanation:

Answer 2

The missing step and reason is $tan(x+x) = \frac{tan(x) + tan(x) }{1-tan(x) tan(x)}$  and

Reason is Tangent sum identity

What is the formula of  identity tan(x+y)?

Formulas for the tangent function can be derived from similar formulas involving the sine and cosine.

$tan(x+y) = \frac{tan(x) + tan(y) }{1-tan(x) tan(y)}$

According to the question

A 2-column table with 3 rows.

Column 1 : row 1 :  tangent (2 x) = tangent (x + x)  

reason given as addition

Column 1 : row 2:

Need to fill next step

i.e

By using  formula of identity tan(x+y)

$tan(x+y) = \frac{tan(x) + tan(y) }{1-tan(x) tan(y)}$

substituting the value

$tan(x+x) = \frac{tan(x) + tan(x) }{1-tan(x) tan(x)}$

Reason : Tangent sum identity

Hence,  the missing step and reason is $tan(x+x) = \frac{tan(x) + tan(x) }{1-tan(x) tan(x)}$  and

Reason is Tangent sum identity

To know more about identity tan(x+y) here:

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