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Rufina [12.5K]
2 years ago
6

Given: Cosine (x minus y)

Mathematics
1 answer:
Lady bird [3.3K]2 years ago
6 0

The required steps that complete the proof are:

Step 1: Cofunction Identity

Step 5: Sine Difference Identity

Step 6: Cofunction Identity

Step 7: Cosine Function Is Even, Sine Function Is Odd

<h3>Trigonometry identity</h3>

Given the cosine function expressed as:

  • cos(x - y)

The first step is to apply the cofunction identity as shown:

  • Step 1: Cofunction Identity

cos(90 - x) = sin x

cos(x - y) = sin (90-(x-y))

  • Step 5: Sine Difference Identity

For the fifth step, you will apply the sine difference identity.

  • Step 6: Cofunction Identity

To get the sixth step, you will apply the Cofunction Identity on the result in the fifth step.

The final step 7 will be

  • Step 7: Cosine Function Is Even, Sine Function Is Odd

Learn more on trigonometry identity here: brainly.com/question/24496175

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There would be 12 people at the party!

In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.

This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.

Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.

Hope this helps!

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