2sinAcosB Formula

Trigonometric Ratios

Trigonometric ratios are ratios of sides in a triangle and there are six trigonometric ratios. In a right-angle triangle, the six trigonometric ratios are defined as:...

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....

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)...

sin 2A Formula Using 2sinAcosB Formula

We have, 2 sin A cos B = sin (A + B) + sin (A – B) Now, let us consider that A = B ⇒ 2 sin A cos A = sin (A + A) + sin (A – A) ⇒ 2 sin A cos A = sin 2A + sin 0° ⇒2 sin A cos A = sin 2A {Since sin 0° = 0} Hence, sin 2A = 2 sin A cos A...

Problems on 2sinAcosB Formula

Problem 1: Express 5 sin 2x cos 6x in terms of the sine function....

FAQs on 2sinAcosB Formula

What is the Formula of 2sinAcosB?...