Double Angle Formulas Double Angle Formulas we shall discuss trigonometric formula which is known as double angle formula. Double angle formulas so called because they involve trigonometric functions of the double angles like sin 2A, cos 2A and tan 2A. The double-angle formulas can be useful when we need to simplify complicated trigonometric expressions. It is better to workout with double-angle formulas, rather than trying to remember the actual formulas. Double Angle Formula Examples Below are the examples based on double-angle formulas Example 1 : Solve the equation cos2x = sin x, for values of x in the interval –π ≤ x < π. Solution : Using double angle formula cos2x = 1 - 2 sin2 x
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Then given equation becomes 1 - 2 sin2 x = sin x This can be rewritten as: 0 = 2 sin2 x + sin x - 1 This is a quadratic equation in the variable sin x. It can be factorized as follows: 0 = (2 sin x - 1)(sin x + 1) It follows that one or both of these brackets are equal to zero, so either 2 sin x - 1 = 0 or sin x + 1 = 0 => sin x = 12 or sin x = -1. Proof of double angle formula: Let A be the angles in the identities. => Put 2A = A + A Now 1. sin(2A) = sin(A + A) = sin A cos A + cos A sin A => sin(2A) = 2sin A cos A 2. cos(2A) = cos(A + A) = cos A cos A - sin A sin A Learn More :- Adding and Subtracting Rational Expressions Math.Tutorvista.com
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=> cos(2A) = cos2A - sin2A 3. tan(2A) = tan(A + A) = tanA+tanA1â&#x2C6;&#x2019;tanA.tanA. tan(2A) = 2tanA1â&#x2C6;&#x2019;tan2A.
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