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3 years ago

Which expression is equivalent to sec2xcot2x?

Mathematics

1 answer:

hram777 [196]3 years ago

5 0

Answer:

B. csc²(x)

Step-by-step explanation:

You can use the relations ...

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = cos(x)/sin(x)

to replace the functions in your expression. Then you have ...

sec²(x)·cot²(x) = (1/cos(x)·cos(x)/sin(x))² = (1/sin(x))² = csc²(x)

___

Alternate solution

You can also use the relation

cot(x) = csc(x)/sec(x)

Then ...

(sec(x)·cot(x))² = (sec(x)·csc(x)/sec(x))² = csc²(x)

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3 years ago

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2 years ago

Karim wants to buy a shirt that normally sells for $46.50. It is on sale for One-third off. How much does Karim need to pay to b

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Step-by-step explanation:

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4 years ago

Read 2 more answers

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago