Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!

Futhe Mathematics <img src="https://tex.z-dn.net/?f=%28Cos%20%7B%7D%5E%7B4%7Dt%20-Sin%20%7B%7D%5E%7B4%7Dt%20%29%20%20%5Cdiv%2

Nastasia [14]

Answer:

cos2t/cos²t

Step-by-step explanation:

Here the given trigonometric expression to us is ,

$\longrightarrow \dfrac{cos^4t - sin^4t }{cos^2t }$

We can write the numerator as ,

$\longrightarrow \dfrac{ (cos^2t)^2-(sin^2t)^2}{cos^2t }$

Recall the identity ,

$\longrightarrow (a-b)(a+b)=a^2-b^2$

Using this we have ,

$\longrightarrow \dfrac{(cos^2t + sin^2t)(cos^2t-sin^2t)}{cos^2t}$

Again , as we know that ,

$\longrightarrow sin^2\phi + cos^2\phi = 1$

Therefore we can rewrite it as ,

$\longrightarrow \dfrac{1(cos^2t - sin^2t)}{cos^2t}$

Again using the first identity mentioned above ,

$\longrightarrow \underline{\underline{\dfrac{(cost + sint )(cost - sint)}{cos^2t}}}$

Or else we can also write it using ,

$\longrightarrow cos2\phi = cos^2\phi - sin^2\phi$

Therefore ,

$\longrightarrow \underline{\underline{\dfrac{cos2t}{cos^2t}}}$

And we are done !

$\rule{200}{4}$

Additional info :-

Derivation of cos²x - sin²x = cos2x :-

We can rewrite cos 2x as ,

$\longrightarrow cos(x + x )$

As we know that ,

$\longrightarrow cos(y + z )= cosy.cosz - siny.sinz$

So that ,

$\longrightarrow cos(x+x) = cos(x).cos(x) - sin(x)sin(x)$

On simplifying,

$\longrightarrow cos(x+x) = cos^2x - sin^2x$

Hence,

$\longrightarrow\underline{\underline{cos (2x) = cos^2x - sin^2x }}$

$\rule{200}{4}$

7 0

2 years ago

Please explain how to find the simplest form of 7/28! I did it in 5th grade but forgot! Explain please.

Lapatulllka [165]

$\sf \frac{7}{28} = \frac{7 \times 1}{7\times 4}\\ We~can~divide~by~7~on~both~the~numerator~and~denominator\\\frac{7\times 1\div 7}{7\times 4\div 7} = \frac{1}{4}$

So in simplest form it would be 1/4

6 0

3 years ago

Read 2 more answers

In the figure below, which term best describes point A?

Sophie [7]

the center of gravity of all triangles is at the intersection of the three midlines.

2) The area of the three boy gogle fermed by the line from the center of gravity of the triangle to each verten is equal, which is 1/3 of the area of the origiend briangle. 6o we can see that selecting option. 60 C is shown in figura.

the answer is c

7 0

2 years ago

Read 2 more answers

Population density is a measure of how crowded an area is. The population density of Australia is approximately 7.6 people per s

meriva

Answer:

B

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

The points A(3, 4), B(3, -2), C(-5, -2), and D(-5, 4) form rectangle ABCD. Which point is halfway between A and B?

Dmitriy789 [7]

Answer: " (3,1) is the point that is halfway between A and B. "
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Explanation:
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We know that there is a "straight line segment" along the y-axis between
"point A" and "point B" ; since, we are given that:
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1) Points A, B, C, and D form a rectangle; AND:

2) We are given the coordinates for each of the 4 (FOUR points); AND:

3) The coordinates of "Point A" (3,4) and "Point B" (3, -2) ; have the same "x-coordinate" value.
________________________________________________
We are asked to find the point that is "half-way" between A and B.
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We know that the x-coordinate of this "half-way" point is three.

We can look at the "y-coordinates" of BOTH "Point A" and "Point B".
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which are "4" and "-2", respectively.

Now, let us determine the MAGNITUDE of the number of points along the "y-axis" between "y = 4" and y = -2 .

The answer is: "6" ; since, from y = -2 to 0 , there are 2 points, or 2 "units" from y = -2 to y = 0 ; then, from y = 0 to y = 4, there are 4 points, or 4 "units".

Adding these together, 2 + 4 = 6 units.
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So, the "half-way" point would be 1/2 of 6 units, or 3 units.
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So, from y = -2 to y = 4 ; we could count 3 units between these points, along the "y-axis". Note, we could count "2" units from "y = -2" to "y = 0".
Then we could count one more unit, for a total of 3 units; from y = 0 to y = 1; and that would be the answer (y-coordinate of the point).
______________________________________________
Alternately, or to check this answer, we could determine the "halfway" point along the "y-axis" from "y = 4" to "y = -2" ; by counting 3 units along the "y-axis" ; starting starting with "y = 4" ; note: 4 - 3 = 1 ; which is the "y-coordinate" of our answer; that is: "y = 1" ; and the same y-coordinate we have from the previous (aforementioned) method above.
______________________________________________
We know the "x-coordinate" is "3" ; so the answer:
_________________________________________________
" (3,1) is the point that is halfway between A and B ."
__________________________________________________

8 0

4 years ago