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4 years ago

4 ( 8n - 1 ) = 19 + 32n

Mathematics

1 answer:

ZanzabumX [31]4 years ago

3 0

Answer:

no variable

Step-by-step explanation:

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How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)

Oxana [17]

Answer:

Make use of the fact that as long as $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ :

$\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ .

$\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}$ .

$\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ .

Step-by-step explanation:

Assume that $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ .

Make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ and $\csc(\theta) = (1) / (\sin(\theta))$ to rewrite the given expression as a combination of $\sin(\theta)$ and $\cos(\theta)$ .

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}$ .

Since $\cos(\theta) \ne 0$ :

$\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

By the Pythagorean identity, $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ . Rearrange this identity to obtain:

$\sin^{2}(\theta) = 1 - \cos^{2}(\theta)$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

Again, make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ to obtain the desired result:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}$ .

5 0

2 years ago

Savanna is ordering crafts for Thanksgiving for her class. Each individual craft cost $1.50. There are a shipping fee and handli

d1i1m1o1n [39]

Answer:

i smell penys

Step-by-step explanation:

3 0

3 years ago

Rectangle ABCD has vertices A(1, 2), B(4, 2), C(1, - 2), and D(4, - 2). A dilation with a scale factor of 6 and centered at the

Rom4ik [11]

Answer:

I'll show you the dilution of point A and you can figure out the answer

Step-by-step explanation:

not sure what level you are in at school. Since the dilation is about the origin, it very straight forward. Basically you multiply the scale factor by each coordinate of a given point.

so the dilated point for A is in the x direction 1x6 and in the y direction 2x6, resulting in A'= (6,12).

do this for each point and you will have the answer

5 0

3 years ago

A student is attempting to solve a multi-step equation. Sample mathematical work is shown below. Which statement best applies to

barxatty [35]

Answer:

Step-by-step explanation:

A: The student incorrectly divided both sides by 35. The student should first add 10 to both sides, obtaining 35x = 15, and then divide 15 by 35, obtaining the final answer 3/7.

7 0

3 years ago

(-2)+5x+(-2x)-2x+(-4)+3

jek_recluse [69]

Answer:X=-3

Step-by-step explanation:

5 x -2x -2x -2-4+3

3 0

4 years ago