All categories

3 years ago

Verify the identity. cot^2x/ cscx-1 = 1+sinx/sinx

1 answer:

8 0

Cot²x /(cscx + 1) = (1 - sinx) /sinx

let's apply the identity cot²x = csc²x - 1:

(csc²x - 1) /(cscx + 1) = (1 - sinx) /sinx

(factoring csc²x - 1 as a difference of squares and then simplifying)

[(cscx + 1)(cscx - 1)] /(cscx + 1) = (1 - sinx) /sinx

cscx - 1 = (1 - sinx) /sinx

let's recall that cscx = 1 /sinx:

(1 /sinx) - 1 = (1 - sinx) /sinx

ending with:

(1 - sinx) /sinx = (1 - sinx) /sinx (verified)

I hope it helps

You might be interested in

Brianna is going to a carnival that has games and rides. Each game costs $1.25 and each ride costs $3.75. Brianna spent $18.75 a

maxonik [38]

Answer:

6 games and 3 rides

Step-by-step explanation:

Let the number of games Brianna played be x,

and the number of rides she went on be y.

Total cost for games= 1.25x

Total cost for rides= 3.75y

Since number of games is twice the number of rides,

x= 2y -----(1)

Total costs= cost of games +cost of rides

$18.75= 1.25x +3.75y$

Multiply the whole equation by 4 to remove the decimals:

$75= 5x +15y$

Simplify by dividing the whole equation by 5:

$15 = x + 3y$

Label the equation:

x +3y= 15 -----(2)

Although we can solve these 2 equations by substitution, since the question requires us to graphically solve, we have to graph 2 linear lines.

I will choose 3 points to plot on the graph for each equation:

x= 2y -----(1)

$\begin{tabular}{|c|c|c|c|} \cline{1-4}x & 2(1) = 2&2(2) = 4&2(3) = 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}$

x +3y= 15 -----(2)

x= -3y +15

$\begin{tabular}{|c|c|c|c|} \cline{1-4}x & -3(1)+15= 12& -3(2)+15= 9& -3(3)+15= 6\\ \cline{1-4}y & 1 &2&3\\ \cline{1-4}\end{tabular}$

Let's plot these points on a graph paper. Then, join them with a straight line for each straight line graph. Please see the attached picture for the graph.

From (1): y= ½x

From (2): 3y= 15 -x

y= 5 -⅓x

From the graph, the solution of the equation is (6,3). The solution is the point on the graph in which the 2 lines intersect.

x- coordinate: 6

y- coordinate: 3

Thus, Brianna played 6 games and went on 3 rides.

8 0

4 years ago

Read 2 more answers

The equation 1/reserve rate= money multiplier shows the relationship between the reserve rate and the money multiplier, regardle

yKpoI14uk [10]

Answer:true

Step-by-step explanation: apex

7 0

3 years ago

A parallelogram's area is given by the expression 4x2 + 2x + 6. The height of the parallelogram is 2x2. what is the base of the

yawa3891 [41]

A = B × h
A = 4x^2 + 2x + 6
h = 2x^2
B = A/h
B = (4x^2 + 2x + 6)/(2x^2)
B = (2x^2 + x + 3)/x^2

7 0

4 years ago

Read 2 more answers

A navy submarine descended at a rate of 4 feet per second. a. Write the descent rate as an integer. b. Write an expression to fi

Rasek [7]

Answer:

1200

Step-by-step explanation:

Since the value they are asking for is in minutes, we need to convert seconds to minutes. We can do that by multiplying 4 and 60, because there are 60 seconds in a minute, and we need to find the value of one minute. Also because the value they gave is 4. When we do this, we get 240. To get the final answer, we need to multiply 240 and 5, because 240 is the descending rate per minute, and they are asking for 5 minutes. When we do this, we get 1200.

(I might get this wrong, so like yeah.)

5 0

3 years ago

What is the solution set for the inequality Negative one-fourthx2(x – 4)(x +5) ≤ 13?

Kitty [74]

Answer:

Step-by-step explanation:

7 0

3 years ago