Rewrite 2tan 3x in terms of tan x.

2 answers:

7 0

The answer is 2(3tan(x)-tan^3(x))/(1-3tan^2(x)) but it is a very long and tedious calculation using alot of trig identities.

Anastasy [175]3 years ago

3 0

We shall use the identity
tan(x+y) = (tanx + tany)/(1 - tanx tany)
Therefore
tan(3x) = tan(2x+x) = [tan(2x)+tan(x)]/[1 -tan(2x) tan(x)]
tan(2x) = (tanx +tanx)/(1 - tan^2x)

That is
tan(3x) = [(2tanx/(1-tan^2x} + tanx]/[1 - tanx(2tanx)/(1-tan^2x)]
= [2tanx + tanx(1-tan^2x)][(1-tanx)(1-tan^2x) + 2 tan^2x]
= [2tanx + tanx - tan^3x]/[1-tan^2x - tanx + tan^3x + 2tan^2x]
= [3tanx - tan^3x]/[1 - tanx + tan^2x + tan^3x]

2 tan3x = [6tanx - 2tan^3x]/[1 - tanx + tan^2x + tan^3x]

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-12x2 + 45x + 12

bazaltina [42]

Answer:

3(4x + 1)(x - 4) Answer choice B

Step-by-step explanation:

-12x^2 + 45 + 12

You would take out the -3 in the equation.

-3(4x^2 -15x - 4)

You can then multiply the first 4 and the last -4 and get a -16. You can then find two numbers that would multiply to -16 and add to -15.

You would do this by listing the factors of -16, which the numbers 1 and -16 would work.

You would then substitute each value in for the 17x and add them together, which this is just separating the value 17x.

3(4x^2 - 16x + x - 4)

3(4x^2 - 16x)(x - 4)

You can then take ou ta four for the first function in the parentheses.

3(4x(x - 4) 1(x - 4))

Then you take the function from the outside and the inside.

3(4x + 1)(x - 4)

The answer to the question would be B.

8 0

3 years ago

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KonstantinChe [14]

The answer is -root 2

Mark as brainliest plz.

8 0

3 years ago

Two friends are collecting cards. Frank has 7 more than half the number of cards as his friend. Together they have 42 cards. How

Naddika [18.5K]

Answer:

The number of cards Frank has is 18 and the number of cards his friend has is 24.

Step-by-step explanation:

The correct question is

Two friends are collecting cards. Frank has 6 more than half the number of cards as his friend. Together they have 42 cards. How many cards does each friend have?

Let

x ----> the number of cards that Frank has

y ----> the number of cards that his friend has

we know that

Together they have 42 cards

$x+y=42$ ----> equation A