All categories

3 years ago

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)

Mathematics

1 answer:

creativ13 [48]3 years ago

4 0

Answer:

(sin^2 w + 1) / cos w.

Step-by-step explanation:

Note: sec w = 1 / cos w and csc w = 1/ sin w.

So we have:

(sec w(1 + csc^2 w)) / (csc^2 w)

= 1/cos w ( 1 + 1/ sin^2 w) / (1 / sin^2 w)

= ( 1/ cos w + 1 / sin^2 w cos w) * sin^2 w

= sin^2 w/ cos w + sin^2 w / (sin^2 w cos w)

= sin^2 w / cos w + 1 / cos w

= (sin^2 w + 1) / cos w.

You might be interested in

Witch one of these is correct

Lady bird [3.3K]

42:105 is the answer

4 0

3 years ago

Read 2 more answers

You borrow $1900 to buy a refrigerator. The simple interest rate is 11%. You pay off the loan after 5 years. How much do you pay

leonid [27]

I = PRT is the formula to use for this.

I = (1900)(.11)(5)
I = 1045

1900 + 1045 = 2945

I need to pay $2945 for the refrigerator.

7 0

3 years ago

The greater of two numbers is 5 more than the smaller. If the

xenn [34]

Answer:

First number = 4

Second number = 9

Step-by-step explanation:

If the first number = x, the second number = x + 5.

The calculation can be expressed as follows:

x + 2(x + 5) = 22

First, expand the bracket 2(x + 5):

x + 2x + 10 = 22

Combine like terms:

3x + 10 = 22

Subtract 10 from both sides:

3x = 12

Divide both sides by 3:

x = 4

First number = 4

Second number = 4 + 5 = 9

5 0

1 year ago

You are paid $9.25/hr at your part-time job. You work 12 hours per week. You are considering working a part-time job for $5.90/h

Sergio039 [100]

It will be over 1 dollar because of the plus

8 0

3 years ago

Read 2 more answers

When 2(3/5 x + 2/3 y - 1/4 x -1 1/2 y + 3 )is simplified, what is the resulting expression?

vovangra [49]

Answer:

Simplifying the expression: $2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)$ we get $\mathbf{42x-100y-360}$

Step-by-step explanation:

We need to simplify the expression: $2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)$

First we will solve terms inside the bracket

$2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)$

Converting mixed fraction $1\frac{1}{2} y$ into improper fraction, we get: $\frac{3}{2}y$

Replacing the term:

$2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-\frac{3}{2}y +3)$

Now, taking LCM of: 5,3,4,2 we get 60

Now multiply 60 with each term inside the bracket

$2(\frac{3}{5}x\times60+\frac{2}{3}y\times60-\frac{1}{4}x\times60-\frac{3}{2}y\times60 +3\times60)\\2(3x\times12+2y\times20-1x\times15-3x\times30-3\times60)\\2(36x+40y-15x-90y-180)$

Now, combine like terms

$2(36x-15x-90y+40y-180)\\2(21x-50y-180)$

Now, multiply all terms with 2

$42x-100y-360$

So, Simplifying the expression: $2(\frac{3}{5}x+\frac{2}{3}y-\frac{1}{4}x-1\frac{1}{2}y +3)$ we get $\mathbf{42x-100y-360}$

3 0

3 years ago

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)​

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w(1+ csc^2 w))/(csc^2 w)