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4 years ago

Prove the identity.

Mathematics

1 answer:

Delvig [45]4 years ago

5 0

Answer:

D. Pythagorean

Step-by-step explanation:

Given the identity

cos²x - sin²x = 2 cos²x - 1.

To show that the identity is true, we need to show that the left hand side is equal to right hand side or vice versa.

Starting from the left hand side

cos²x - sin²x ... 1

According to Pythagoras theorem, we know that x²+y² = r² in a right angled triangle. Coverting this to polar form, we have:

x = rcostheta

y = rsintheta

Substituting into the Pythagoras firnuka we have

(rcostheta)²+(rsintheta)² = r²

r²cos²theta+r²sin²theta = r²

r²(cos²theta+sin²theta) = r²

(cos²theta+sin²theta) = 1

sin²theta = 1 - cos²theta

sin²x = 1-cos²x ... 2

Substituting equation 2 into 1 we have;

= cos²x-(1-cos²x)

= cos²x-1+cos²x

= 2cos²x-1 (RHS)

This shows that cos²x -sin²x = 2cos²x-1 with the aid of PYTHAGORAS THEOREM

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Write an equation in slope intercept form of the line with a slope of -3/4 and y intercept of -5

raketka [301]

Given,
slope(m)=-3/4
y intercept (c)=-5
Then,
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3 years ago

Simplify the expression to one number using order of operations:

geniusboy [140]

<h2><u>COMBINED OPERATIONS</u></h2><h3>Exercise</h3>

First, let's solve the subtraction (in parentheses):

$\mathsf{\dfrac{-8\left(2-6\right)}{2}}$

$\mathsf{\dfrac{-8(-4)}{2}}$

Now, let's solve the multiplication. Remember: in multiplication, two negative numbers will give a positive number:

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Finally, let's solve the division:

$\mathsf{\dfrac{32}{2} = 16}$

<h3><u>Answer</u>: 16</h3>

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3 years ago

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Ratling [72]

Answer:

Choice number one:

$\displaystyle \frac{5}{10}\cdot \frac{4}{9}$ .

Step-by-step explanation:

Let $A$ be the event that the number on the first card is even.
Let $B$ be the event that the number on the second card is even.

The question is asking for the possibility that event $A$ and $B$ happen at the same time. However, whether $A$ occurs or not will influence the probability of $B$ . In other words, $A$ and $B$ are not independent. The probability that both $A$ and $B$ occur needs to be found as the product of

the probability that event $A$ occurs, and
the probability that event $B$ occurs given that event $A$ occurs.

5 out of the ten numbers are even. The probability that event $A$ occurs is:

$\displaystyle P(A) = \frac{5}{10}$ .

In case A occurs, there will only be four cards with even numbers out of the nine cards that are still in the bag. The conditional probability of getting a second card with an even number on it, given that the first card is even, will be:

$\displaystyle P(B|A) = \frac{4}{9}$ .