SOLUTION: Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°

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Question 1018132: Write the expression as the sine, cosine, or tangent of an angle.
cos 112° cos 45° + sin 112° sin 45°

Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Write the expression as the sine, cosine, or tangent of an angle.
cos 112° cos 45° + sin 112° sin 45°
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1.
cos(112°)*cos(45°) + sin(112°)*sin(45°) = cos(112°)*cos(-45°) - sin(112°)*sin(-45°) =          

                                          Apply the formula for cos of the sum of angles for 112° and -45°
                                          See the lesson Addition and subtraction formulas in this site.


= cos(112° - 45°) = cos(67°).


2.
Of which angle?



Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
Write the expression as the sine, cosine, or tangent of an angle.
cos 112° cos 45° + sin 112° sin 45°
The above is the "Difference of two angles" identity, as: cos+%28A+-+B%29+=+cos+%28A%29+cos+%28B%29+%2B+sin+%28A%29+sin+%28B%29
Therefore,
cos+%28112+-+45%29, or highlight%28highlight_green%28highlight%28cos+%2867%5Eo%29%29%29%29 = cos+%28112%5Eo%29+cos+%2845%5Eo%29+%2B+sin+%28112%5Eo%29+sin+%2845%5Eo%29