All categories

1 year ago

Prove the identities (sec^2-1)cot^2=1

Mathematics

1 answer:

In-s [12.5K]1 year ago

6 0

The trigonometric Identity proof (sec²θ - 1)cot²θ = 1 is as explained below.

<h3>How to prove trigonometric Identities?</h3>

We want to prove that;

(sec²θ - 1)cot²θ = 1

Now, we know from trigonometric identities that;

sec²θ - 1 = tan²θ

Thus, the left hand side of our original equation can be written as;

tan²θ * cot²θ

We also know in trigonometric identities that 1/tan θ = cot θ. Thus;

tan²θ * cot²θ can be written as;

tan²θ * (1/ tan²θ)

The above will cancel out to give us 1 which is also equal to the right hand side and as such our trigonometric proof is complete.

Read more about Trigonometric Identities at; brainly.com/question/7331447

#SPJ1

You might be interested in

What is an algebraic expression that has no like terms and no parentheses is in this form

vaieri [72.5K]

"Simplest form is the one <span>algebraic expression that has no like terms and no parentheses is in this form. This is actually the simplest way of describing an algebraic expression. I hope that this is the answer that you were looking for and it has actually come to your desired help.</span>

8 0

3 years ago

Read 2 more answers

Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of 4 and labeled it

Novay_Z [31]

Answer:

The area of triangle K is 16 times greater than the area of triangle J

Step-by-step explanation:

we know that

If Triangle K is a scaled version of Triangle J

then

Triangle K and Triangle J are similar

If two triangles are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

Ak ------> the area of triangle K

Aj -----> the area of triangle J

$z^{2}=\frac{Ak}{Aj}$

we have

$z=4$

substitute

$4^{2}=\frac{Ak}{Aj}$

$16=\frac{Ak}{Aj}$

$Ak=16Aj$

therefore

The area of triangle K is 16 times greater than the area of triangle J

4 0

2 years ago

Read 2 more answers

The archway of the main entrance of a university is modeled by the quadratic equation

Scilla [17]

Answer:

B. (1,5) and (5.25, 3.94)

Step-by-step explanation:

The answer is where the 2 equations intersect.

We need to solve the following system of equations:

y = -x^2 + 6x

4y = 21 - x

From the second equation:

x = 21 - 4y

Plug this into the first equation:

y = -(21 - 4y)^2 + 6(21 - 4y)

y = -(441 - 168y + 16y^2)+ 126 - 24y

y = -441 + 168y - 16y^2 + 126 - 24y

16y^2 + y - 168y + 24y + 441 - 126 = 0

16y^2 - 143y + 315 = 0

y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)

y = 5, 3.938

When y = 5:

x = 21 - 4(5) = 1

When y = 3.938

x = 21 - 4(3.938) = 5.25.

3 0

3 years ago

Evaluate the expression when a= 4, b= - 2, and c= 7 - -> 5a - 9 (b - c)

ollegr [7]

Answer:

$65$

Step-by-step explanation:

Given the following question:

$5a-9(b-c)$
a = 4
b = 2
c = 7

In order to find the answer, we need to substitute the variables with the numbers given, and then solve using PEMDAS.

$5\times4-9\times(2-7)$
$2-7=-5$
$5\times4-9\times-5$
$5\times4=20$
$20-9\times-5$
$9\times-5=-45$
$20--45$
$20+45=65$
$=65$

Hope this helps.