All categories

2 years ago

Simplify (sinx + cosx) ^2/ sin2x

Mathematics

1 answer:

Aleksandr [31]2 years ago

8 0

$\csc 2x+1$

Step-by-step explanation:

$\frac{(\sin x+\cos x)^2}{\sin2x}$

We expand $(\sin x+\cos x)^2$ using algebraic identity $(a+b)^2=a^2+b^2+2ab$

$=\frac{\sin^2x+\cos^2x+2\sin x.\cos x}{\sin2x}$

$= \frac{1+\sin2x}{\sin2x}$

$=\frac{1}{\sin2x}+\frac{\sin2x}{\sin2x}$

$=\csc 2x+1$

You might be interested in

Layla and Sam are both dog sitters. Layla charges $2 per day plus a sign-up fee of $3. Sam charges a flat rate of $3 per day. Th

Nikolay [14]

Answer:

Givens

Layla charges $2 per day, plus a sign-up fee of $3. Notice the sign-up fee represents a fixed value, that's gonna be the constant form of the function. And $2 is the ratio of change of the function, because it a cost per day.
Sam charges $3 per day, without extra fee. So, the ratio of change of this function is $3, and it doesn't have a constant term.

According to the given information, the linear function for Layla is:

$f(x)=2x+3$

Notice that the constant ratio of change is coefficient of the independent variable, that is, because that variable represents days, and each charges $2.

On the other hand, the linear function for Sam is:

$g(x)=3x$

As we said before, this expression doesn't have any constant term, because the charges are flate $3 per day, it's just that rate.

Now, to find the number of days needed to both Layla and Sam earn the same money, we just have to solve the equation $f(x)=g(x)$

$2x+3=3x\\3=3x-2x\\x=3$

Therefore, on day three they are gonna earn the same amount of money.

3 0

3 years ago

Read 2 more answers

How do you get the answer for 2 7/10- 1 1/4

IRISSAK [1]

Answer:

Step-by-step explanation:

Convert the fraction to decimals by dividing

7/10 = 0.7 add 2 = 2.7

1/4 = 0.25 add 1 = 1.25

2.7 - 1.25 = 1.45 = 1 9/20

I'm always happy to help :)

4 0

4 years ago

Can someone help me

KatRina [158]

Let's recall that in a parallelogram:

1. The opposite sides are paralell

In our exercise. sides CZ and KG are paralell. And so do sides KC and GZ.

2. Those opposite sides are equal in length.

3. The opposites angles are equal. In our exercise, angle C and G are equal and so do angles K and Z.

4. That also mean that the angles at the top of the figure are supplementary. It means they add up to 180 degrees. We have the same situation with the two angles at the bottom of the parallelogram.

In our case then:

$\angle\text{ C = }\angle\text{ G }\Rightarrow\text{ C = 50}\circ\text{ , G = 50}\circ$

Now, we can find the measure of angles K and Z, as follows:

$\angle C\text{ + }\angle Z\text{ = 180}\Rightarrow\text{ 50 + }\angle Z\text{ = 180 }\Rightarrow\text{ }\angle Z\text{ = 180 - 50}$ $\angle Z\text{ = 130}\circ\text{ }\Rightarrow\angle K\text{ = 130}\circ$

3 0

1 year ago

Solve for x. Round your answer to the nearest tenth

seraphim [82]

${x}^{2} = {24}^{2} - {23}^{2} \\ \\ {x}^{2} = 576 - 529 \\ \\ {x}^{2} = 47 \\ \\ x = \sqrt{47}$