Using the Addition Formulas

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Question

Using the Addition Formulas

Use the addition formulas to derive the identities in Exercises 31–36.

cos (x − π/2) = sin x

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Using the sine addition formula, solve for sign of X plus pi divided by 4. Awesome. So it appears for this particular problem we're asked to use the sine addition formula to help us solve for sign of X plus pi divided by 4. So now that we know what we're trying to solve for, let's read off our multiple choice answers to see what our final answer might be. A is the square rooted 2 multiplied by sin of X minus cosine of X. B is the square rooted 2 multiplied by sin of x plus cosine of x. C is the square rooted 2 divided by 2, all multiplied by sin of x minus cosine of X. And finally, D is square rooted 2 divided by 2, all multiplied by sin of x plus cosine of x. Fantastic. So, first off, let us recall and use the sine addition formula, and the sine addition formula states that sign of A plus B. And once again we need to note that sign of A plus B is going to be equal to sign of a multiplied by cosine of B. Plus. Cosign of A. Multiplied by sign of B. Fantastic. So now we need to note that for this particular problem, A is going to be equal to X. And B is going to be equal to pi divided by 4. So we plug in our values for A and B into our expression. Based on the information that's provided to us by the prom itself, we'll be able to write that sign of X plus pi divided by 4 is going to be equal to drum roll, sign of X. Multiplied by the square rooted 2 divided by 2. Plus cosine of X multiplied by the square rooted 2 divided by 2. Fantastic. And once again, that's when we plug in our values of X in for A and B, which is so when we plug in pi divided by 4 in for B. So, when we factor out the square to 2 divided by 2 out, we will find that Sign of X plus pi divided by 4 is going to be equal to the square rooted 2 divided by 2, all multiplied by the sign of X plus the cosine of X, and that is our final answer. Hooray, we did it. So therefore, when we solve for sign of X plus pi divided by 4, we will find that it's equal to. The square root of 2 divided by 2, all multiplied by sin of x plus cosine of X, and this corresponds with multiple choice answer letter D, which once again is the square root of 2 divided by 2, all multiplied by the sin of x plus cosine of x. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Using the Addition Formulas

Use the addition formulas to derive the identities in Exercises 31–36.

cos (x − π/2) = sin x

Key Concepts

Addition Formulas

Trigonometric Identities

Co-function Identities

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