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3 years ago

PageProve thatTan ( 2 Tan^-l x)=2 Tan ( Tan^-1 x + Tan^-1 x^3)

Mathematics

1 answer:

Kay [80]3 years ago

5 0

Answer:

The answers are 0, 1 and −2.

Step-by-step explanation:

Let α=arctan(2tan2x) and β=arcsin(3sin2x5+4cos2x).

sinβ2tanβ21+tan2β2tanβ21+tan2β23tanxtan2β2−(9+tan2x)tanβ2+3tanx(3tanβ2−tanx)(tanβ2tanx−3)tanβ2=3sin2x5+4cos2x=3(2tanx1+tan2x)5+4(1−tan2x1+tan2x)=3tanx9+tan2x=0=0=13tanxor3tanx

Note that x=α−12β.

tanx=tan(α−12β)=tanα−tanβ21+tanαtanβ2=2tan2x−13tanx1+2tan2x(13tanx)or2tan2x−3tanx1+2tan2x(3tanx)=tanx(6tanx−1)3+2tan3xor2tan3x−3tanx(1+6tanx)

So we have tanx=0, tan3x−3tanx+2=0 or 4tan3x+tan2x+3=0.

Solving, we have tanx=0, 1, −1 or −2.

Note that −1 should be rejected.

tanx=−1 is corresponding to tanβ2=3tanx. So tanβ2=−3, which is impossible as β∈[−π2,π2].

The answers are 0, 1 and −2.

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svetoff [14.1K]

Answer:

7 units

Step-by-step explanation:

$\sqrt{|-3-4|^{2}-|4-4|^{2}}$

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3 years ago

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Pls helpppppp this stuff makes no sense

yulyashka [42]

Answer:

x = 5

Step-by-step explanation:

a || b and a line intersecting them is their transversal.

$\therefore m\angle 1=m\angle 5\\(corresponding \:\angle 's) \\\\\therefore 60 - 2x = 70 - 4x\\\\\therefore 4x - 2x = 70 - 60\\\\\therefore 2x = 10\\\\\therefore x =\frac{10}{2} \\\\\huge \orange {\boxed {\therefore x = 5}}$

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3 years ago

Progress

irina [24]

An expression represents the perimeter, in centimeters, of this triangle is 6q + 8r - 5s.

<u>Given the following data:</u>

a = (q + r) centimeters.

b = (5q - 10s) centimeters.

c = (5s + 7r) centimeters.

<h3>What is a triangle?</h3>

A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

<h3>How to calculate the perimeter of a triangle?</h3>

Mathematically, the perimeter of a triangle can be calculated by using this formula:

P = a + b + c

<u>Where:</u>

a, b, and c are length of sides.

Substituting the given parameters into the formula, we have;

P = q + r + 5q - 10s + 5s + 7r

P = 6q + 8r - 5s centimeters.

Read more on perimeter of triangle here: brainly.com/question/27109587

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1 year ago

7(x + 4) + 5(x-6) please expand and simplify

Neporo4naja [7]

Answer:

12x − 2

Step-by-step explanation:

7(x+4)+5(x−6)

Distribute:

=(7)(x) + (7)(4) + (5)(x) + (5)(−6)

=7x + 28 + 5x − 30

Combine Like Terms:

=7x + 28 + 5x − 30

=(7x+5x) + (28−30)

= 12x − 2

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3 years ago

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2x+3y=1 and y=-2 - 9 solve using linear combination method. Please explain steps.

kaheart [24]

Answer:

$x=17$

Step-by-step explanation:

$2x+3y=1$

$y=-2-9$

In order to combine these two equations, an idea you need to keep in mind is finding a way of setting these equations as equal to each other. I saw that each equation shared a common value, $y$ . In this case, we need to isolate $y$ in the first equation so that both equations $=y$ .

$2x+3y=1$

$3y=-2x+1$

$\frac{3y}{3}=\frac{-2x+1}{3}$

$y=-\frac{2}{3}x+\frac{1}{3}$

With this, we now know that both $-2-9$ and $-\frac{2}{3}x+\frac{1}{3}$ are equal to $y$ , so we can set them equal to each other.

$y=-\frac{2}{3}x+\frac{1}{3}$

$y=-11$

$-\frac{2}{3}x+\frac{1}{3}=-11$

Reply to this if anything I'm saying or doing is confusing in any way, or if you find a mistake. :) Solve for $x$ .

$-\frac{2}{3}x+\frac{1}{3}=-11$

$-\frac{2}{3}x=-11-\frac{1}{3}$

$-\frac{2}{3}x =-\frac{33}{3}-\frac{1}{3}$

$-\frac{2}{3}x =-\frac{34}{3}$

$-\frac{2}{3}x(-\frac{3}{2})=-\frac{34}{3}(-\frac{3}{2})$

$x=\frac{102}{6}=17$

$x=17$

Hopefully this answer is correct AND makes sense in terms of how I achieved it. Again, reply to this with any questions or mistakes I made and I'll do my best to answer or fix them.

4 0

2 years ago

PageProve thatTan ( 2 Tan^-l x)=2 Tan ( Tan^-1 x + Tan^-1 x^3)​

PageProve thatTan ( 2 Tan^-l x)=2 Tan ( Tan^-1 x + Tan^-1 x^3)