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Sphinxa [80]
3 years ago
8

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

Mathematics
2 answers:
earnstyle [38]3 years ago
5 0

Answer:

-cos \ x

Step-by-step explanation:

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

"<em>sine of x to the second power minus one divided by cosine of negative x</em>"

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)

"<em>sine of x </em><em>to the second power</em><em> </em><em>minus</em><em> one </em><em>divided by</em><em> cosine of negative x</em>"

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

slega [8]3 years ago
4 0

Answer:

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)

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