In Exercises 5–8, each expression is the right side of the formul...

Question

In Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β.

b. Write the expression as the cosine of an angle.

cos 50° cos 20° + sin 50° sin 20°

Accepted Answer

Hello, today we're going to be simplifying the given trigonometric expression. So what we are given is cosine of 70 degrees multiplied by cosine of 10 degrees plus sine of degrees multiplied by sine of 10 degrees. Now, we do have a method in simplifying this given expression, we can use the difference property for cosine the difference property for cosine states that if you have cosine of A minus B, this can be expanded to cosine of a multiplied by cosine of B plus sine of A multiplied by sign of B. Now we're going to be using this property going from right to left in order to simplify the expression. But before we simplify the expression, let's identify our A and our B values a trick in doing this is to note that the first cosine and sine values have the same angle. And the second cosine and sine values have the same angle. If we take a look at our given expression, the first cosine and sine values have an angle of 70 degrees. So we're going to allow A to equal to 70 degrees. Furthermore, the second cosine and sine values have an angle of 10 degrees. So we're going to allow B to equal to 10 degrees. Now, if we use the property to simplify the expression, we can simplify the expression as cosine of 70 minus 10 and 70 minus 10 is going to give us 60. So the simplified form of the expression is going to be cosine of degrees. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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In Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. b. Write the expression as the cosine of an angle. cos 50° cos 20° + sin 50° sin 20°