Find the exact value of each expression. See Example 1.
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Question

Find the exact value of each expression. See Example 1.

sin 40° cos 50° + cos 40° sin 50°

Accepted Answer

Hey, everyone in this problem, we're asked to determine the exact value of the following trigonometric expression. And we're given sine of 25 degrees cosine of 65 degrees plus cosine of 25 degrees sine of 65 degrees. We have four answer choices. Option A zero, option B one, option C negative one and option D two. So we have sign of something multiplied by cosine of something plus cosine of something multiplied by s of something. Let's recall our identity for the addition of angles with sign. OK. If we have sign of some angle A plus B, we can write this as sign, OK? Multiplied by cosine of B plus cosine of a multiplied by sine of B. Now this thing on the right hand side is exactly what we have in the expression we were given. OK? But in this case, our A value is 25 degrees and our B value it's 65 degrees. OK? So we're gonna take A to be 25 degrees, we're gonna take B to be 65 degrees. And when we do that, we can write sign of 25 degrees multiplied by cosine of 65 degrees was cosign of 25 degrees multiplied by sign of 65 degrees as sign of 25 degrees plus 65 degrees. OK. So we had this whole messy expression and we were able to simplify it into a single sign function. Now that we have this single sine function, we can go ahead and simplify. So 25 degrees plus 65 degrees gives us 90 degrees. So we have that this is equal to s of 90 degrees sine of 90 degrees we know is equal to just one. And so we were able to take this messy expression and simplify it all the way down to just one. OK. So the correct answer here is going to be option B Thanks everyone for watching. I hope this video helped see you in the next one.

Find the exact value of each expression. See Example 1.
sin 40° cos 50° + cos 40° sin 50°

Key Concepts

Trigonometric Identities

Sine and Cosine Functions

Angle Relationships

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