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3 years ago

Verify the identity. cot x / 1 + csc x = csc x - 1 / cot x

Mathematics

1 answer:

svetlana [45]3 years ago

5 0

Step-by-step explanation:

cot x / (1 + csc x)

Multiply by conjugate:

cot x / (1 + csc x) × (1 − csc x) / (1 − csc x)

Distribute the denominator:

cot x (1 − csc x) / (1 − csc²x)

Use Pythagorean identity:

cot x (1 − csc x) / (-cot²x)

Divide:

(csc x − 1) / cot x

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3 years ago

Suppose PR = 54, solve for QR 4x-1 3x-1 P R

Svet_ta [14]

Answer:

$QR = 23$

Step-by-step explanation:

P, A, and R are collinear.

PR = 54

$PQ = 4x - 1$

$QR = 3x - 1$

To solve for the numerical length of PR, let's generate an equation to find the value of x.

According to the segment addition postulate:

$PQ + QR = PR$

$(4x - 1) + (3x - 1) = 54$ (substitution)

Solve for x

$4x - 1 + 3x - 1 = 54$

Combine like terms

$4x + 3x - 1 - 1 = 54$

$7x - 2 = 54$

Add 2 to both sides

$7x - 2 + 2 = 54 + 2$

$7x = 56$

Divide both sides by 7

$\frac{7x}{7} = \frac{56}{7}$

$x = 8$

$QR = 3x - 1$

Plug in the value of x into the equation

$QR = 3(8) - 1 = 24 - 1$

$QR = 23$

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3 years ago

2. Jessica's grandparents gave her $2000 for college to put in a savings account until she starts

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Answer:

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Step-by-step explanation:

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3 years ago

D, h, and p are coplanar ?

Allushta [10]

Answer:

Yes

Step-by-step explanation:

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3 years ago

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2.) If ZA = (20 – 2m)º and ZD = (m – 130°, what is the value of m?

vivado [14]

Answer:

m = 50

Step-by-step explanation:

∠ D and ∠ A are vertically opposite angles and are congruent , then

m - 130 = 20 - 2m ( add 2m to both sides )

3m - 130 = 20 ( add 130 to both sides )

3m = 150 ( divide both sides by 3 )

m = 50

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2 years ago

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