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]

You might be interested in

Find the slope-intercept form between the two points (0,-4) and (-3,-10) * 2 points<br> Your answer

sattari [20]

Answer:

Y=2x-4

Step-by-step explanation:

3 0

2 years ago

Determine whether the statements are True or False. Justify your answer with an explanation.

frez [133]

Problem 1

<h3>Answer: False</h3>

---------------------------------

Explanation:

The notation (f o g)(x) means f( g(x) ). Here g(x) is the inner function.

So,

f(x) = x+1

f( g(x) ) = g(x) + 1 .... replace every x with g(x)

f( g(x) ) = 6x+1 ... plug in g(x) = 6x

(f o g)(x) = 6x+1

Now let's flip things around

g(x) = 6x

g( f(x) ) = 6*( f(x) ) .... replace every x with f(x)

g( f(x) ) = 6(x+1) .... plug in f(x) = x+1

g( f(x) ) = 6x+6

(g o f)(x) = 6x+6

This shows that (f o g)(x) = (g o f)(x) is a false equation for the given f(x) and g(x) functions.

===============================================

Problem 2

<h3>Answer: True</h3>

---------------------------------

Explanation:

Let's say that g(x) produced a number that wasn't in the domain of f(x). This would mean that f( g(x) ) would be undefined.

For example, let

f(x) = 1/(x+2)

g(x) = -2

The g(x) function will always produce the output -2 regardless of what the input x is. Feeding that -2 output into f(x) leads to 1/(x+2) = 1/(-2+2) = 1/0 which is undefined.

So it's important that the outputs of g(x) line up with the domain of f(x). Outputs of g(x) must be valid inputs of f(x).

7 0

3 years ago

JO. Jeff buys 3 boxes of cereal for $2.99 each a gallon of

kramer

First add up the total of the food. Then, multiply it by .2 (20%), and subtract that number from your total. You will get the price Jeff paid for his food.