Mathematics, 26.06.2019 19:00 coolcat3190

Simplify the expression. sine of x to the second power minus one divided by cosine of negative x

Answers: 1

Show answers

Answers

Answer from: pillgiing

the answer is the letter a) -sin x

Step-by-step explanation:

Simplify the expression.

sine of x to the second power minus one divided by cosine of negative x

(1−sin2(x))/(sin(x)−csc(x))

sin2x+cos2x=11−sin2x=cos2x

cos2(x)/(sin(x)−csc(x))csc(x)=1/sin(x)cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))sin2(x)− 1=-cos2(x)cos2(x)/(( -cos2(x))/sin(x))

=-sin(x)

Answer from: jerria73

$-cos \ x$

Step-by-step explanation:

First of all, we must have to understand what is the described expression in the paragraph

"sine of x to the second power minus one divided by cosine of negative x"

In this sentence, we need to identify what are the elements and operations involved in the expression.

In the sentence appears ""to the second power", "minus" and "divided by" (highlighted)

"sine of x to the second power minus one divided by cosine of negative x"

Therefore, the expression must has three operations:

"to the second power": refers to exponentiation"minus": refers to a substraction"divided by": refers to a division

Now, we can identify what are the elements: "sine of x", "one" and "cosine of negative x"

"sine of x": refers to $sin\ x$ "one": refers to the number one (1)"cosine of negative x": refers to cos (-x)

Therefore, the expression is:

$\frac{(sin\ x)^{2}-1}{cos(-x)}$

In order to find the simplified expression, we must have to apply these trigonometric identities:

$(sin\ x)^{2} = sin^{2}x$ $sen\x^{2}x \ +\ cos\x^{2}x=1$ $cos(-x)=cos\ x$

Applying the first and third identities, we have:

$\frac{(sin\ x)^{2}-1}{cos(-x)}=\frac{sin\x^{2}x-1}{cos\ x}$

From the second trigonometric identity, we have:

$cos\x^{2}x=\ 1-sin\x^{2}x$

Now, multiplying by -1 in both sides:

$(-1)(cos\x^{2}x)=(-1)(1-\ sin\x^{2}x)$

In the left side, multiplying by -1 the sign of the expression changes:

$(-1)(cos\x^{2}x)=-cos\x^{2}x$

In the right side, multiplying by -1 changes the order of the substraction:

$(-1)(1-\ sin\x^{2}x)=\ sin\x^{2}x-1$

Putting all together:

$-cos\x^{2}x=\ sin\x^{2}x-1$

Now, replacing values we have:

$\frac{sin\x^{2}x-1}{cos\ x}=\frac{-cos\x^{2}x}{cos\ x}=-\frac{cos\x^{2}x}{cos\ x}$

Finally, the property of the first trigonometric identity (property of exponentiation) can be apply in this case:

$-\frac{cos\x^{2}x}{cos\ x}=-\frac{(cos\ x)^{2}}{cos\ x}=-cos\ x$

Answer from: Quest

“exterior angles of triangles. an exterior (or external) angle is the angle between one side of a triangle and the extension of an adjacent side. try this drag the orange dots on any vertex to reshape the triangle.” look to get to the answer i explained what it means and other things i hope it you .
Which is the beat definition of an exterior angle of a triangle

Which is the beat definition of an exterior angle of a triangle

Answer from: Quest

answer: options

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:30

It says factor each expression completely 8y+48

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Stefano accidentally dropped his sunglasses off the edge of a canyon as he was looking down. the height, h(t), in meters (as it relates to sea level), of the sunglasses after t seconds, is shown in the table. during its descent, the pair of sunglasses passed by a climber in the canyon 6 seconds after stefano dropped them. to the nearest meter, what is difference in elevation between stefano and the climber? 166 meters 176 meters 230 meters 240 meters its b.176 i took the test 166 is wrong and 176 is correct

Answers: 1

Answer

Mathematics, 21.06.2019 19:10

What are the coordinates of the point that is 1/3 of the way from a to b? a (2,-3) b (2,6)

Answers: 3

Answer

Mathematics, 21.06.2019 20:30

Twelve less than a number is at most 20

Answers: 1

Answer

You know the right answer?

Simplify the expression. sine of x to the second power minus one divided by cosine of negative x...