Derivation of 2sinasinb formula
We can derive the 2sinasinb formula with the help of the sum and difference of formulae of the cosine function.
- cos (A + B) = cos A cos B – sin A sin B ———— (1)
- cos (A – B) = cos A cos B + sin A sin B ———— (2)
Now subtract the equation(1) from the equation (2)
⇒ cos (A – B) – cos (A + B) = [cos A cos B + sin A sin B] – [cos A cos B – sin A sin B]
⇒ cos (A – B) – cos (A + B) = cos A cos B + sin A sin B – cos A cos B + sin A sin B
⇒ cos (A – B) – cos (A + B) = sin A sin B + sin A sin B
⇒ cos (A – B) – cos (A + B) = 2 sin A sin B
Hence, 2 sin A sin B = cos (A – B) – cos (A + B)
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2sinAsinB Formula
2sinasinb is one of the important trigonometric formulas which is equal to cos (a – b) – cos (a + b). 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
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