Product To Sum
We found 6 formulas for product to sum
Express the product of sine, cosine and tanegent functions as a sum of trigonometric functions.
1.
Product of sines
$\sin\alpha \cdot \sin \beta = \dfrac{1}{2} \left[ \cos(\alpha-\beta) - \cos(\alpha + \beta) \right]$
2.
Product of cosines
$\cos\alpha \cdot \cos \beta = \dfrac{1}{2} \left[ \cos(\alpha-\beta) + \cos(\alpha + \beta) \right]$
3.
Product of sine and cosine
$\sin\alpha \cdot \cos \beta = \dfrac{1}{2} \left[ \sin(\alpha-\beta) + \sin(\alpha + \beta) \right]$
4.
Product of tangents
$\tan\alpha \cdot \tan\beta = \dfrac{\tan \alpha + \tan \beta}{\cot \alpha + \cot \beta}$
5.
Product of cotangents
$\cot\alpha \cdot \cot\beta = \dfrac{\cot \alpha + \cot \beta}{\tan \alpha + \tan \beta}$
6.
Product of tangent and cotangents
$\tan\alpha \cdot \cot\beta = \dfrac{\tan\alpha + \cot\beta}{\cot\alpha+\tan\beta}$