Practice Problems on Sum to Product Formulas
Problem 1: Solve: sin 10y – sin 6y.
Problem 2: Prove that: (cos 8x + cos 6x) / sin 2x = 2 cot 2x cos 14x.
Problem 3: Evaluate: (cos 4a – cos 2a) / (cos 4a + cos 2a).
Problem 4: Evaluate: sin 15° + sin 45°.
Sum to Product Formulas
The sum to product formulas are trigonometric identities that convert the sum or difference of two trigonometric functions into a product of trigonometric functions. These formulas are particularly useful in simplifying expressions, solving trigonometric equations, and integrating functions.
Sum to Product formulas are important formulas of trigonometry. Four sum-to-product formulas in trigonometry are,
- sin A + sin B = 2 sin [(A+B)/2] × cos [(A-B)/2]
- sin A – sin B = 2 cos[(A+B)/2] × sin[(A-B)/2]
- cos A + cos B = 2 cos[(A+B)/2] × cos[(A-B)/2]
- cos A – cos B = 2 sin[(A+B)/2] × sin[(A-B)/2]
In this article, we will learn about Sum to Product Formulas, Proof of Sum to Product Formulas, Application of Sum to Product Formulas in detail.
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