Derivation of 2sinAcosB Formula
From the sum and difference formulae of trigonometry, we have,
sin (A + B) = sin A cos B + sin B cos A ⇢ (1)
sin (A – B) = sin A cos B – sin B cos A ⇢ (2)Now, by adding equations (1) and (2) we get,
⇒ sin (A + B) + sin (A – B) = (sin A cos B + sin B cos A) + (sin A cos B – sin B cos A)
⇒ sin (A + B) + sin (A – B) = sin A cos B + sin A cos B
⇒ sin (A + B) + sin (A – B) = 2 sin A cos B
Therefore, 2 sin A cos B = sin (A + B) + sin (A – B)
2sinAcosB Formula
2sinacosb is one of the important trigonometric formulas which is equal to sin (a + b) + sin (a – b). It is one of the product-to-sum formulae that is used to convert the product into a sum.
This formula is derived using the angle sum and angle difference formulas. Before learning more about the 2sinAsinB Formula, let’s first learn in brief about, Trigonometric Ratios
Table of Content
- Trigonometric Ratios
- 2sinAcosB Formula
- Derivation of 2sinAcosB Formula
- sin 2A Formula Using 2sinAcosB Formula
- Problems on 2sinAcosB Formula
- FAQs on 2sinAcosB Formula
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