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3 years ago

Can anyone help me with this

Mathematics

1 answer:

ANTONII [103]3 years ago

4 0

Answer:

Sure, what do you need

Step-by-step explanation:

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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

3 years ago

The equation of a line is y=4x+7 write down the gradient of the line and write down the y-intercept of the line.

Mandarinka [93]

Compare with the general form of the slope intercept of a line:-

y = mx + b

slope m = 4 and y-intercept b = 7

6 0

3 years ago

3 x1/4 = Please help me

elena-14-01-66 [18.8K]

Answer:

3/4

Step-by-step explanation:

please mark me as brainliest

8 0

3 years ago

Read 2 more answers

A basketball player's "hang time" is the amount of time the player remains suspended in the air after a jump. The height (in met

matrenka [14]

Answer:

The graph is a nonlinear function. Michael Jordan's hang time is 0.9 seconds. The maximum height is about 1 meter. For t between t = 0.5 and t = 1, the height is decreasing.

Step-by-step explanation:

Okay the first one: It's nonlinear because its not a line, its a curve and its definitely not constant. The curve on the graph stops at (0.9,0) so his hangtime is 0.9 seconds. The peak of the curve is about 1 meter. Pretty self explanatory. And the last one, after the point 0.5, the height of the curve goes down, so it is decreasing.

4 0

3 years ago

What is the slope and 7-intercept of the line on the graph below? B= m= write an equation for this line in slope-intercept form

victus00 [196]

Answer:

B=m2+72

Step-by-step explanation:

5 0

3 years ago