Triple the sum of 33 and 27

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 HELP

LekaFEV [45]

Answer: one solution

Step-by-step explanation:

CONCEPT:

- One solution is when the final variable would be able to find a solution.

- Infinite solution is when the equations result in 0=0, meaning any number will fit

- No solution is when the equation results in both sides on equal.

SOLVE:

Given

3/4x-7=3(1/6x+1)

Expand Parenthesis

3/4x-7=1/2+3

Multiply both sides by the LCM of fractions (Least Common Multiple)

4(3/4x-7)=4(1/2x+3)

3x-28=2x+12

Subtract both sides by 2x

3x-28-2x=2x+12-2x

x-28=12

Add both sides by 28

x-28+28=12+28

x=40

Since we are able to get exactly one solution, there is only one solution.

Hope this helps!! :)

Please let me know if you have any quesionts

5 0

3 years ago

Let f(x) = x2 − 2x − 3. The secant line through (2, f(2)) and (2 + h, f(2 + h)) for f(x) has slope h + 2. Use this formula to co

Mkey [24]

Answer:

a) slope of secant line = 3

b) slope of tangent line = 2

Step-by-step explanation:

Given:

- The function:

f(x) = x^2 -2*x - 3

- The slope for f(x) @ x = 2 is:

slope = h + 2

Find:

a) The slope of the secant line through (2, f(2)) and (3, f(3))

b) The slope of the tangent line at x = 2

Solution:

- Since we are given the slope of the line computed via secant method. All we need to do is evaluate the slope given for respective question.

- The slope of secant line between points ( 2 , f(2) ) and ( 3 , f(3) ) is:

slope = h + 2

Where, h is the step size between two points. h = 3 - 2 = 1

slope = 1 + 2 = 3

Hence, the slope of the secant is 3.

- The slope of tangent line @ points ( 2 , f(2) ) is:

slope = Lim _ h-->0 (h + 2)

Where, h step size is reduced to infinitesimal small number. Hence, h = 0

slope = 0 + 2 = 2

Hence, the slope of the tangent is 2.

5 0

4 years ago

A circle has a diameter of 5. What is the area and circumference.

Aloiza [94]

Answer:

Area= 19.63 units squared Circumference= 15.71 units

Step-by-step explanation:

Area= π r ^2

Circumference= 2π r

3 0

3 years ago

Read 2 more answers

80/36 as a mixed number

Blababa [14]

Answer:

yes because the one on top is larger than the number on the bottom

3 0

3 years ago