Name the property shown by the statement. 2 + 5 = 7

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

Y = - 2x + 1 2x - 2y = 4 Solve systems of equations by substitutions

astraxan [27]

Answer:

x= 1

y= -1

Step-by-step explanation:

y=-2x+1

2x-2y=4

substitute for y

2x-2(-2x+1)=4

reduce

2x+4x-2=4

6x=6

x=1

y= -2(1)+1

y= -1

6 0

2 years ago

Answer, please. I need help.

Ghella [55]

Answer:

-8x^12

Step-by-step explanation:

When you have an exponent outside of parenthesis, it is raising everything in the parenthesis to that exponent (in this case, the third). The first step to solve this is to multiply the exponents in the parenthesis by 3. This is called the power of a power rule.

-2 is being raised to the first power. 1x3 = 3, and x is being raised to the fourth power. 4x3 = 12, so you now have:

-2^3x^12

You can simplify -2^3: -2 x -2 x -2 = -8

This leaves you with -8x^12

You can check this by putting -8x^12 and (-2x^4)^3 into a graphing calculator. You know that you simplified correctly if they show the same graphs.

7 0

2 years ago

300 ml of an IV fluid contains 50 mcg of Drug A. If a patient is receiving 1000 ml of this IV fluid, how much of Drug A is this

Harlamova29_29 [7]

Answer: 166.666 mcgs

Step-by-step explanation:

3 0

2 years ago

Question 1 of 10

Liula [17]

Answer:

B

Step-by-step explanation:

A P E X

5 0

2 years ago