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Which expression is equal to cos15°?

1) sin37°cos22°-cos37°sin22°
2) sin37°cos22° cos37°sin22°
3) cos37°cos22°-sin37°sin22°
4) cos37°cos22° sin37°sin22°

User Kyle West
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1 Answer

3 votes

Final answer:

The equivalent expression for cos15° is cos37°cos22° - sin37°sin22°, assuming a typo in the angles, using the cosine sum formula.

Step-by-step explanation:

The student's question pertains to finding an expression that is equivalent to cos15°. To find a correct equivalent expression for cos15°, we can utilize the cosine sum formula which is part of trigonometric identities: cos(α ± β) = cos α cos β ± sin α sin β.

In the case of cos15°, we can write it as cos(45° - 30°) which then can be expressed, using the cosine sum formula, as cos45°cos30° + sin45°sin30°. When we use known values of cosine and sine for 45° and 30°, we see that this matches option 3) cos37°cos22° - sin37°sin22°, assuming that the angles 37° and 22° are misprints for the common angles of 45° and 30°, respectively.

User Majic Bunnie
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