For each expression in Column I, use an identity to choose an ...

Question

For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.

cos 75°

Accepted Answer

Hello, everyone. We are asked which of the following expressions is equivalent to the cosine of 112 degrees. Our answer choices are a negative cosine of 112 degrees B two sine 56 degrees cosine 56 degrees C negative square root of the fraction one plus the cosine of 224 degrees divided by two D one divided by the KC can of 112 degrees. So we have a lot of different identities that we have been using. Let's go through our answer choices and see which ones match an identity that we have correctly. So first for a, if we're thinking about odd and even identities, we could say that the cosine of negative X equals the cosine of X, but this is saying it equals the negative cosine of X. So this does not work for B. This looks very similar to two sine of a cosine of A which is the double angle identity for shine. But we're not working with sign, we're working with cosign. So that one doesn't work either for C this looks very much like the half angle identity for cosine. So the cosine of a divided by two would equal plus or minus the square root of one plus the cosine of a divided by two. So for this to be true, we need to see if this is the right. A, so the cosine of a divided by two would have to equal the cosine of 112 degrees. So a divided by two would have to equal 112 degrees, multiplying both sides by two. It would have to be 224 degrees which it is um let's verify that it should be negative. So 112 degrees is in quadrant two and in quadrant two, cosine is negative. So, so far answer choice C looks like it is the correct answer. But let's check the, just in case for D, this appears like we are using a reciprocal identity. The problem is the cosine of theta is equal to one divided by the C can of theta, not the Kosi can of theta. So answer choice D also does not work. So C answer choice C is our answer negative square root of the fraction one plus the cosine of 224 divided by two. Have a nice day.

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For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
cos 75°