Sin 3x Formula Expand the term on the right hand side using the binomial theorem viz cos 3x i sin 3x cos 3 x 3i cos 2 x sin x 3 sin 2 x cos x i sin 3 x So equating imaginary parts and you
Since this is cos 3x i sin3x we can conclude that cos3x cos 3x 3 cos x sin 2x and sin3x 3 cos 2x sin x sin 3x You can simplify with the Pythagorean Since the angle sum formula of sine is sin alpha beta sinalphacosbeta cosalphasinbeta and the double angle formula of cosine
Sin 3x Formula
Sin 3x Formula
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Derive Triple Angle Trigonometric Formula Sin3x From Compound Angle
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What Is The Integral Of Sin 3 x Epsilonify
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The answers are cos3x 4cos 3x 3cosx and sin3x 3sinx 4sin 3x We need cos 2x sin 2x 1 According to Demoivre s theorem cosx isinx n cosnx isinnx Here n 3 So I and using the reduction integral formula for sin 7x cos 3x My steps
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Using de Moivre s formula to find an expression for sin 3x in terms of sin x and cos x 1 Since the angle sum formula of sinus sin alpha beta sinalphacosbeta cosalphasinbeta and the double angle formula of cosine
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Expand the term on the right hand side using the binomial theorem viz cos 3x i sin 3x cos 3 x 3i cos 2 x sin x 3 sin 2 x cos x i sin 3 x So equating imaginary parts and you
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Since this is cos 3x i sin3x we can conclude that cos3x cos 3x 3 cos x sin 2x and sin3x 3 cos 2x sin x sin 3x You can simplify with the Pythagorean
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Sin 3x Formula - The answers are cos3x 4cos 3x 3cosx and sin3x 3sinx 4sin 3x We need cos 2x sin 2x 1 According to Demoivre s theorem cosx isinx n cosnx isinnx Here n 3 So
