Write 2sin37(degrees)sin26(Degrees) as a sum (or difference)
To express 2sin37°sin26° as a sum or difference, we will first need to use the trigonometric identity known as the product-to-sum formula.
The product-to-sum formula states that for two angles A and B, sin(A)sin(B) can be expressed as:
sin(A)sin(B) = (1/2)[cos(A - B) - cos(A + B)]
Using this formula, we can rewrite 2sin37°sin26° as follows:
2sin37°sin26° = 2 * (1/2)[cos(37° - 26°) - cos(37° + 26°)]
Simplifying further, we have:
= [cos(37° - 26°) - cos(37° + 26°)]
Hence, the expression 2sin37°sin26° can be written as a difference of two cosine terms.