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3 years ago

Cot^2x csc^2x + 2 csc^2x –cot^2 = 2

Mathematics

1 answer:

kow [346]3 years ago

4 0

Answer:

x = π/2 + πk

Step-by-step explanation:

cot² x csc² x + 2 csc² x − cot² x = 2

Multiply both sides by sin² x:

cot² x + 2 − cos² x = 2 sin² x

Add cos² x to both sides:

cot² x + 2 = 2 sin² x + cos² x

Pythagorean identity:

cot² x + 2 = sin² x + 1

Subtract 1 from both sides:

cot² x + 1 = sin² x

Pythagorean identity:

csc² x = sin² x

Multiply both sides by sin² x:

1 = sin⁴ x

Take the fourth root:

sin x = ±1

Solve for x:

x = π/2 + 2πk, 3π/2 + 2πk

Which simplifies to:

x = π/2 + πk

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3 years ago

Answer the questions below about the quadratic function.

Korolek [52]

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2 years ago

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Step-by-step explanation:

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1 year ago

Assuming boys and girls are equally likely, find the probability of a couple having a baby girl when their sixth child is born

Ivanshal [37]

Answer: The required probability of having 6th girl is 0.5.

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We are to find the probability of a couple having a baby girl when their sixth child is born, given that the first five children were all girls.

Since the events of having a boy and a girl are independent of each other, so

the probability of having 6th girl dose not depend on the birth of the first five girls.

We know that there are only two possible cases (either a boy or girl will born).

So, sample space, S = {G, B} and the event E of having a girl is, E = {G}.

That is, n(S) = 2 and n(E) = 1.

Therefore, the probability of event E is given by

$P(E)=\dfrac{n(E)}{n(S)}=\dfrac{1}{2}=0.5.$

Thus, the required probability of having 6th girl is 0.5.

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2 years ago