2sinAcosB Formula
2sinacosb is one of the product-to-sum formulae. Similarly, we have three other products to sum/difference formulas in trigonometry, namely, 2sinasinb, 2cosacosb, and 2cosasinb. By using the 2sinacosb formula, we can simplify trigonometric expressions and also solve integrals and derivatives involving expressions of the form 2sinacosb.
This trigonometric identity is derived by adding the sin (a + b) and sin (a – b) identities. And the formula for the same is shown in the image added below:
The 2sinacosb formula is,
2 sin A cos B = sin (A + B) + sin (A – B)
From the formula, we can observe that product of a sine function and a cosine function is converted into a sum of two other sine functions. For example,
The product-to-sum formulae for half angles are,
2 sin (x/2) cos (y/2) = sin [(x + y)/2] + sin [(x – y)/2]
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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