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3 years ago

Is the work shown in the simplification below correct? Explain. csc(t) sec(t) = 1 cos(t) ÷ 1 sin(t) = 1 cos(t) • sin(t) 1

2 answers:

4 0

No, because it states csc(t) x sec(t), not divide, so therefore it would result to (1/cos(t)) x (1/sin(t)) if simplified

bekas [8.4K]3 years ago

3 0

Answer:

Step-by-step explanation:

Alright, lets get started.

Te given expression is:

$csc (t) sec (t)$

Using reciprocal identity, replacing csc into sin term and sec into cos term

$\frac{1}{sin(t)}\frac{1}{cos(t)}$

$\frac{1}{sin(t)cos(t)}$ : Answer

Hope it will help :)

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Please help me answer this question

ratelena [41]

By the definition of the hyperbolic function tanh x, we have proven that $\frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}$

<h3>Hyperbolic functions & Proof of identities </h3>

By definition

$tanh \ x=\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}}$

Then,

$\frac{1-tanh \ x}{1 + tanh \ x}=\frac{1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }{1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} }$

$=1-\frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} \div (1+ \frac{e^{x} -e^{-x}}{e^{x} +e^{-x}} })$

$=\frac{e^{x} +e^{-x}-(e^{x} -e^{-x})}{e^{x} +e^{-x}} \div (\frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} })$

$=\frac{e^{x} +e^{-x}-e^{x} +e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{-x}+e^{x} -e^{-x}}{e^{x} +e^{-x}} }$

$=\frac{e^{-x}+e^{-x}}{e^{x} +e^{-x}} \div \frac{e^{x} +e^{x} }{e^{x} +e^{-x}} }$

$=\frac{2e^{-x}}{e^{x} +e^{-x}} \div \frac{2e^{x} }{e^{x} +e^{-x}} }$

$=\frac{2e^{-x}}{e^{x} +e^{-x}} \times \frac{e^{x} +e^{-x}}{2e^{x}}$

$=\frac{2e^{-x}}{1} \times \frac{1}{2e^{x}}$

$=\frac{2e^{-x}}{2e^{x}}$

$=\frac{e^{-x}}{e^{x}}$
$=e^{-x} \times \frac{1}{e^{x}}$

$= e^{-x} \times e^{-x}$

$= e^{-x+-x}$

$= e^{-x-x}$

$= e^{-2x}$

Hence, we have proven that $\frac{1-tanh \ x}{1 + tanh \ x}=e^{-2x}$

Learn more on Proof of Identities here: brainly.com/question/2561079

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2 years ago

If our visible universe is 144 billion light years in diameter, how many kilometres is this?

balu736 [363]

1.362345188052e+24 Kilometers. Using advanced ladder method.

5 0

4 years ago

3. Simplify the following. Leave your answer in index form.

Andre45 [30]

Answer:

a) 21,952

b) 3,375

c) 36

Step-by-step explanation:

a) 7 X 7 X 7 X 4 X 4 X 4

= 7cube X 4cube

= 343 X 64

= 21,952

b) 5 X 3 X 5 X 3 X 5 X 3( group it)

5 X 5 X 5 X 3 X 3 X 3

= 5cube X 3cube

= 125 X 27

= 3,375

c) 3 X 3 X 2 X 2

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= 9 X 4

= 36

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3 years ago

If f || g, then find the value of x. The diagram is not to scale.

Juli2301 [7.4K]

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8 0

3 years ago

What is the solution to this inequality?<br> –16x > –80

Kisachek [45]

Answer:

x < 5

Step-by-step explanation:

–16x > –80

Divide each side by -16, remembering to flip the inequality

-16x/-16< -80/-16

x < 5

7 0

3 years ago