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Hello everybody.
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In this video, i'm going to be showing you how to solve exercise 17 in chapter 9, section 1 of cohen's pre -calculus 7th edition.
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Now in this problem, they want us to use the first edition formula for cosine to compute the quantity cosine of 75 degrees.
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Now to do this, what we first want to do is recall the first edition formula of the cosine, which deals with addition in its argument.
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For two angles, s and t, the cosine of s plus s.
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Is equal to the cosine of s times the cosine of t minus the sign of s times the sign of t.
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And now, in this formula, what we can do is in this left -hand side, we can set s equal to 45 degrees and t equal to 30 degrees.
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And this gives us the expression cosine of s, which is 45 degrees, plus t.
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Which is 30 degrees.
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And the reason i've written this in this form is because 45 degrees plus 30 degrees is 75 degrees.
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So the result we get from this expansion is going to be the answer to cosine of 70 degrees, 75 degrees as well.
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And so now, using this formula, let's go ahead and expand out this quantity here...