The formula for SinA SinB is derived from the product-to-sum trigonometric identities. It can be expressed as:
SinA SinB = (1/2)[Cos(A - B) - Cos(A + B)]
This formula allows you to express the product of two sine functions as the difference of two cosine functions.
Here's how it works:
- A and B represent two angles.
- Cos(A - B) represents the cosine of the difference between angles A and B.
- Cos(A + B) represents the cosine of the sum of angles A and B.
Practical Insights:
- This formula is useful for simplifying expressions involving the product of sine functions.
- It can be used to solve trigonometric equations and prove trigonometric identities.
Example:
Let's say you want to find the value of Sin30° Sin60°. Using the formula, we get:
Sin30° Sin60° = (1/2)[Cos(30° - 60°) - Cos(30° + 60°)]
= (1/2)[Cos(-30°) - Cos(90°)]
= (1/2)[√3/2 - 0]
= √3/4
Therefore, Sin30° Sin60° = √3/4.
