Can someone help me on number 5!!!

aleksandr82 [10.1K]

This is one pathway to prove the identity.

Part 1

$\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\$

Part 2

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

Part 3

$\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\$

As the steps above show, the goal is to get both sides be the same identical expression. You should only work with one side to transform it into the other. In this case, the left side transforms while the right side stays fixed the entire time. The general rule is that you should convert the more complicated expression into a simpler form.

We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity $\sin^2(\theta)+\cos^2(\theta) = 1$ in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

3 0

3 years ago

Describe the patter and find the next two terms of each sequence <br> 5,1,7,0,9,-1,11

Mila [183]

There are two interleaved arithmetic sequences here.

Odd terms are 5, 7, 9, 11, increasing by 2 each time.

Even terms are 1, 0, -1, decreasing by 1 each time.

The next two terms will be -2, 13.

6 0

4 years ago

Sorry for not putting the picture

Marizza181 [45]

Answer:

Answer bellow

Step-by-step explanation:

9cm⋅12cm=108cm²

17cm=108cm²

7cm=108cm²

9cm=108cm²

3cm=108cm²

4 0

2 years ago

Read 2 more answers

a culture started with 6,000 bateria after 6 hours,it grew to 7,200 .predict how many bacteria will be present after 17 hours ro

Genrish500 [490]

Answer:

10058

Step-by-step explanation:

The equation is of the form

y = ab^x

Where a is the initial value, y is the final amount and x is the time

y = 6000 b^x

7200 = 6000 b^6

Divide each side by 6000

7200/6000 = b^6

1.2 = b^6

Take the 6th root on each side

1.2 ^ 1/6 = b^6 ^ 1/6

1.030853321 = b

y = 6000 (1.030853321) ^ x

Let x = 17

y = 6000 (1.030853321) ^ 17

y=10057.68696

Rounding to the nearest whole number

y = 10058

7 0

3 years ago

Read 2 more answers

A right rectangular prism has a height of 12 in. And the area of its base is 18sq. In. What is the volume of the prism?

asambeis [7]

Answer:

Step-by-step explanation:

Volume = 12 × 18 = 216 in³

7 0

3 years ago