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Novosadov [1.4K]
3 years ago
5

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

Mathematics
2 answers:
Kay [80]3 years ago
6 0
Cot x = cos x csc x
1/tan x = cosx (1/sin x)
1/(sin x / cos x) = cos x / sin x
cos x / sin x = cos x / sin x

The domain of validity is all real number values of x except for sin x = 0.
Ede4ka [16]3 years ago
4 0
<h2>Answer:</h2>

<u>Domain of validity--</u>

All real numbers except nπ where n belongs to integers.

( Since,

\sin n\pi=0\ for\ all\ n\ belonging\ to\ integers )

<h2>Step-by-step explanation:</h2>

We are asked to prove the trignometric identity:

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

We know that the cotangent function is given by the formula:

          \cot \theta=\dfrac{\cos \theta}{\sin \theta}

Also we know that:

\csc \theta=\dfrac{1}{\sin \theta}

Hence, we have:

\cot \theta=\cos \theta\times \dfrac{1}{\sin \theta}\\\\\\\cot \theta=\cos \theta\csc \theta

Now, the domain of validity i.e. the values for which the cotangent function is defined is the set of all the real  number except where sine function is zero.

Since the sine function appear in the denominator and for a function to be well defined denominator term must be non-zero.

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Find the slope of the line 7x+4y=10
Fittoniya [83]

Answer:

The slope is -7/4

Step-by-step explanation:

∵ 7x + 4y = 10

∵ y = mx + c ⇒ where m is the slope of the line

∴ Re-arrange the equation

∴ 4y = 10 - 7x ⇒ ÷4

∴ y = 10/4 - (7/4) x

∴ y = 5/2 - (7/4) x

∴ The slope is -7/4

3 0
3 years ago
I need help with math
Bogdan [553]

A. ∠4 is congruent to ∠5; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

D. ∠2 and ∠3; True.

<h3>What are the properties of angles of parallel lines?</h3>
  • On a common plane, two parallel lines do not intersect.
  • As a result, the characteristics of parallel lines with respect to transversals are given below.
  1. Angles that correspond are equal.
  2. Vertical angles are equal to vertically opposite angles.
  3. Interior angles that alternate are equal.
  4. The exterior angles that alternate are equal.

For the give question;

Two line are cut by the transversal.

∠1 =  90.5° and ∠7  =  89.5°

Thus the result for the given statement are-

A. ∠4 is congruent to ∠5 because they are alternate interior angles; True.

B. Two lines are parallel; True.

C. The measure of ∠6 = 90.5°; False.

∠6 = ∠7 =  89.5°.(correct)

D. ∠2 and ∠3 are supplementary because they are same-side exterior Angeles; True.

Thus, the result for the given statement are found.

To know more about the parallel lines, here

brainly.com/question/4954460

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3 0
1 year ago
1. *
julsineya [31]

Answer:

Her multiplication

Step-by-step explanation:

Not really an aexplanation

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3 years ago
PLEASE HELP ME W THIS QUESTION
snow_lady [41]

Answer:

J

Step-by-step explanation:

If the side of the shape is increased by 3/2 then the total distance around the shape will be 3/2 bigger.

Example: If the pentagon has side length 2 then it becomes 2*3/2 = 6/2 = 3.

The original perimeter was 2+2+2+2+2 = 10.

The new perimeter is 3+3+3+3+3 = 15.

Did you notice that \frac{15}{10}=\frac{3}{2}? J is correct.

3 0
3 years ago
Help me with this one
Artist 52 [7]

9514 1404 393

Answer:

  "complete the square" to put in vertex form

Step-by-step explanation:

It may be helpful to consider the square of a binomial:

  (x +a)² = x² +2ax +a²

The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...

  2a = 1

  a = 1/2

That means we can write ...

  (x +1/2)² = x² +x +1/4

But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:

  x^2+x+1\\\\=(x^2+x+\frac{1}{4})+\frac{3}{4}\\\\=(x+\frac{1}{2})^2+\frac{3}{4}

_____

Another way to consider this is ...

  x² +bx +c

  = x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*

  = (x +b/2)² +(c -(b/2)²)

for b=1, c=1, this becomes ...

  x² +x +1 = (x +1/2)² +(1 -(1/2)²)

  = (x +1/2)² +3/4

_____

* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).

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3 years ago
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