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xz_007 [3.2K]
3 years ago
12

Which fundamental identity is used in the second step of proof?

Mathematics
1 answer:
stepladder [879]3 years ago
4 0

Answer:

C) sin^2(Ф) + cos^2(Ф) = 1

Step-by-step explanation:

sin^2(Ф) - cos^2(Ф)sin^2(Ф) = sin^4(Ф)

LHS = sin^2(Ф) - cos^2(Ф)sin^2(Ф)

Step 1: sin^2(Ф) [ 1 - cos^2(Ф)]

Now we use the identity sin^2(Ф) + cos^2(Ф) = 1 because sin^2(Ф) = 1- cos^2(Ф)

Step 2: Using the above identity

sin^2(Ф) (sin^2(Ф)) = sin^4 (Ф)

Answer: C) sin^2(Ф) + cos^2(Ф) = 1

Hope this will helpful.

Thank you.

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2 years ago
James has a bag 77 of nickels and dimes. The total value of coins is $6.60. How many dimes does James have?
tatuchka [14]

James has 55 dimes in the bag

Step-by-step explanation:

The given is:

  • James has in a bag 77 of nickels and dimes
  • The total value of coins is $6.60

We need to find how many dimes James has

Assume that the number of nickels is x and the number of

dimes is y in the bag

∵ There are x nickels in the bag

∵ There are y dimes in the bag

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∴ x + y = 77 ⇒ (1)

∵ 1 nickel = 5 cents

∴ The value of nickles in the bag = 5x cents

∵ 1 dime = 10 cents

∴ The value of dimes in the bag = 10y cents

∵ The total value of coins is $6.60

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∴ 5x + 10y = 660 ⇒ (2)

Now we have a system of equations to solve it

Multiply equation (1) by -10 to eliminate y

∵ -10x - 10y = -770 ⇒ (3)

- Add equations (2) and (3)

∴ -5x = -110

- Divide both sides by -5

∴ x = 22

Substitute the value of x in equation (2) to find y

∵ 22 + y = 77

- Subtract 22 from both sides

∴ y = 55

∴ The number of dimes is 55

James has 55 dimes in the bag

Learn more:

You can learn more about the system of equations in brainly.com/question/6075514

#LearnwithBrainly

6 0
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