Write 2sin37(degrees)sin26(Degrees) as a sum (or difference)
To write 2sin37°sin26° as a sum or difference, we can use the trigonometric identity called the product-to-sum formula. The formula is as follows:
sin A sin B = (1/2) * [cos(A - B) - cos(A + B)]
Using this formula, we can rewrite 2sin37°sin26° as:
2sin37°sin26° = 2 * (1/2) * [cos(37° - 26°) - cos(37° + 26°)]
Simplifying the expression further:
= [cos(37° - 26°) - cos(37° + 26°)]
Now, let's calculate the values inside the cosine function:
37° - 26° = 11°
37° + 26° = 63°
Substituting these values back into the expression:
= [cos(11°) - cos(63°)]
Therefore, 2sin37°sin26° can be written as:
2sin37°sin26° = cos(11°) - cos(63°)