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To expand an expression using the distributive property, multiply each term inside a set of parentheses by each term outside the parentheses, and then simplify by combining like terms.
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A good method to expand cos(2x) cos (2 x) is by using De Moivre's theorem (r(cos(x)+i ⋅sin(x))n = rn (cos(nx)+i⋅sin(nx))) (r (cos (x) + i ⋅ sin (x)) n = r n (cos (n x) + i ⋅ sin (n x))). When r = 1 r = 1, cos(nx)+i ⋅sin(nx) = (cos(x)+ i⋅sin(x))n cos (n x) + i ⋅ sin (n x) = (cos (x) + i ⋅ sin (x)) n.
Use the double - angle identity to transform cos(2x) cos (2 x) to 2cos2(x)−1 2 cos 2 (x) - 1. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.
Expand (2cos2(x)− 1)(2cos2(x)− 1) (2 cos 2 (x) - 1) (2 cos 2 (x) - 1) using the FOIL Method. Tap for more steps... 2cos2(x)(2cos2(x))+2cos2(x)⋅−1− 1(2cos2(x))− 1⋅−1 2 cos 2 (x) (2 cos 2 (x)) + 2 cos 2 (x) ⋅ - 1 - 1 (2 cos 2 (x)) - 1 ⋅ - 1. Simplify and combine like terms. Tap for more steps... 4cos4(x)−4cos2(x)+ 1 4 cos 4 (x) - 4 cos 2 (x) + 1.
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prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More
Cos2x is an important trigonometric function that is used to find the value of the cosine function for the compound angle 2x. We can express cos2x in terms of different trigonometric functions and each of its formulas is used to simplify complex trigonometric expressions and solve integration problems.
