Verify the basic identity. What is the domain of validity? cot theta = cos theta csc theta

Answers

Answer 1

Answer: Both sides can be the domain of validity since both are just simple but what we are going to change is the right side.
Let us review that $cot \alpha = (cos \alpha )/(sin \alpha )$ and $csc \alpha = (1)/(sin \alpha )$ .
So, to prove the following identity:
$cot \alpha =cos \alpha csc \alpha$
Let us substitute the value of csc with respect to sin.
$cot \alpha =cos \alpha * (1)/(sin \alpha )$
$cot \alpha = (cos \alpha )/(sin \alpha )$
$cot \alpha =cot \alpha$

Answer 2

Answer:

The domain of validity of the given identity is:

All real numbers except nπ where n belongs to integers.

Step-by-step explanation:

We are asked to prove the trignometric identity:

$\cot \theta=\cos \theta\csc \theta$

We know that:

$\cot \theta=(\cos \theta)/(\sin \theta)$

Hence, the function cotangent is defined where the denominator is not zero i.e. all the real numbers except where sine function is zero.

We know that the zeros of sine function are of the type: nπ where n belongs to integers.

Also, we can write the expression by:

$\cot \theta=\cos \theta\cdot (1)/(\sin \theta)$

We know that cosecant function is the reciprocal of the sine function.

i.e.

$\csc \theta=(1)/(\sin \theta)$

Hence, we get:

$\cot \theta=\cos \theta\cdot \csc \theta$

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25 POINTS AND BRAINLIESTSUPER EASY!

Which is the best scale to use when making a line graph for the data below?
Week

1

2

3

4

Profits (in dollars)

228

367

385

280

A) from 0 to 1000

B) from 200 to 1000

C) from 0 to 400

D) from 200 to 400

Answers

it's D from 200 to 400

The answer would be C because it is the most effective interval set.

Mikel creates the table below to help her determine 40% of 70. She writes the expression Which change in Mikel’s expression will lead her to the correct answer?

Answers

Answer:

The 0.2 in the expression could be changed to 2

Step-by-step explanation:

Each column of the table represents:

20% = 0.2 = 14

To determine 40% the expression should be:

2*20% = 2*14

So the correct answer choice is the last one:

The 0.2 in the expression could be changed to 2

The change in the expression to get the correct answer is option B. Mikel should changes the 0.2 in her expression to 0.4.The correct expression for 40% of 70 is (0.4)(70) = 28.

Mikel's expression is (0.2)(14) = 2.8.

The only change that needs to be made to Mikel's expression is to change the 0.2 to 0.4.

This is because 40% is equivalent to 0.4.

So the answer is to change the 0.2 in Mikel's expression to 0.4.

Here is a breakdown of the calculation:

40% of 70

= 40/100 × 70

= 28

(0.2)(14)

= 0.2 × 14

= 2.8

As it can be seen, the only difference between the two expressions is the value of the first factor.

In the correct expression, the first factor is 0.4, while in Mikel's expression, the first factor is 0.2.

Therefore, if Mikel changes the 0.2 in her expression to 0.4, then her expression will be correct.

learn more about expression here

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Algebra 1 taking stock

Answers

Given:

36 inch long pipe

Must be cut into 21/4 inch long pieces

Required:

How many pieces to be cut

Solution:

All you need to do is to divide 36 by 21/4

Dividing this will result to 48/7 pipes or 6 and 6/7 pipes

Solve the system of equations by using the elimination method.2x – 7y = 3
5x – 4y= -6
pls help me

Answers

Answer:

Hi! The correct answer is (-2,-1)!

Step-by-step explanation:

~Add the equations in order to solve for the first variable, Plug this value into the other equations in order to solve for the remaining variables~

Simplify the expressions using the distributive property.8(7x + 3)5(5y - 2)

Answers

Simplify the expressions by using the distributive property.

$\begin{gathered} 8(7x+3)=8\cdot7x+3\cdot8 \n =56x+24 \end{gathered}$

For second expression,

$\begin{gathered} 5(5y-2)=5\cdot5y+5\cdot(-2) \n =25y-10 \end{gathered}$

Compare using <, >, or =.
7/9_____4/9

Answers

< is the answer , trust me

Think of fractions like a pizza pie, the more parts it's cut into the less everyone will have. 7/9 is smaller than 4/9 because of the remainder of what would be left over if this was actual pie.

7/9 is less than (the first symbol) 4/9

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