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xenn [34]
3 years ago
7

I need help proving a few trigonometric identities.

Mathematics
1 answer:
ryzh [129]3 years ago
5 0

Answer:

i have solved them . if u can't understand. .. ask me XD

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Verify the identity cot(x-pi/2)=-tan x
vampirchik [111]
To verify the identity we need the following identities:

i) \displaystyle{ \cot(x)= \frac{\cos x}{\sin x}

ii) \displaystyle{ \sin (x-y)=\ sinx\cdot\ cosy -\ siny\cdot\ cosx

iii) \displaystyle{ \cos (x-y)=\ cosx\cdot \ cosy +\ sinx\cdot\ siny.

Also, we have know that \displaystyle{ \sin \frac{ \pi }{2}=1 and \displaystyle{ \cos \frac{ \pi }{2}=0.


Thus, \displaystyle{ \cot(x-\frac{\pi}{2})= \frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}

By (ii) and (iii) we have:

\displaystyle{ \frac{\cos (x-\frac{\pi}{2})}{\sin (x-\frac{\pi}{2})}= \frac{\ cosx\cdot \ cos\frac{\pi}{2} +\ sinx\cdot\ sin\frac{\pi}{2}}{\ sinx\cdot\ cos\frac{\pi}{2} -\ sin\frac{\pi}{2}\cdot\ cosx} = \frac{\ sinx}{-\cos x}

by simplifying \displaystyle{ \sin \frac{ \pi }{2}=1 and \displaystyle{ \cos \frac{ \pi }{2}=0.

Now, \displaystyle{ \frac{\ sinx}{-\cos x} is clearly -tanx.
4 0
3 years ago
Solve the proportion for x. When applicable, simplify all radicals and show all of your
Sedaia [141]

The simplified radical for the given equation is 2√3.

The given equation is \frac{3}{x} =\frac{x}{4}.

<h3>What are radicals?</h3>

Radical of any number is the same as the root of the number. The root can be a square root, cube root, or in general, it is nth root. Thus, any expression or number that uses a root is known as a radical.

To compute for the values of x given the proportion, we can cross-multiply both sides of the equation as follows:

\frac{3}{x} =\frac{x}{4}

⇒x×x=3×4

⇒x²=12

⇒x=±√12

From this, we can see that the solutions for the equation are the positive and negative roots of 12.

By simplifying the radical, we get √12 = √(2² x 3) = 2√3

Therefore, the simplified radical for the given equation is 2√3.

To learn more about radicals visit:

brainly.com/question/1369233.

#SPJ1

3 0
2 years ago
A new york city taxi charges $3 per ride plus an additional $0.50 per mile which function below shows how to calculate the total
RideAnS [48]

Answer: The correct answer is Choice C.

Step-by-step explanation: The cost of the ride is .50 per mile, plus $3.00 for each ride. In order to calculate it, the correct formula is going to multiply the number of miles, represented by x, by .50, and then add $3 for the ride.

Choice C is doing just that. $.50x + $3

4 0
3 years ago
Which situation describes a non-proportional relationship?
Pani-rosa [81]

Situation of non- proportional relationship :

The circumference of a circle with a radius of x units can be represented by = 2nx.

The perimeter of an equilateral triangle with a side length of x  units can be represented by y = 3x

The total surface area of a cylinder with a radius of 1 unit and height of x units can be represented by y = 2xx + 2x

The radius of a circle with a diameter of x units can be represented by y = \frac{1}{2}x

a proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant. The graph of a proportional relationship is a line through the origin.

When ratios between quantities are not constant, a relationship may be linear but not proportional and the graph does not pass through the origin.

The graph shows the sales tax charged based

on the amount spent at a video game store in

a particular city. Does the graph show a linear

relationship? Is the relationship proportional

or nonproportional?

The graph shows a linear proportional

relationship because it is a line that contains

the origin.

learn more about non-proportional relationship here :brainly.in/question/26595752

SPJ9

8 0
2 years ago
3x^4y^2+15x^3y^3 factor please
AlexFokin [52]

Answer:

3xy( {x}^{3} y + 5 {x}^{2}  {y}^{2} )

3 0
3 years ago
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