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What is the formula of SinA SinB?

Published in Trigonometry 1 min read

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.

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