sinx cos 2x 0 sin x sin frac x 2 0 0 le x le 2 pi cos x sin x 0 sin 4 theta frac sqrt 3 2 0 forall 0 le theta
Use the important double angle identity sin2x 2sinxcosx to start the solving process Explanation 2sinxcosx cosx 0 sin 4x cos x 0 2sin 2x cos 2x cos x 0 Trigonometry Solve for cos 2x sin x 0 cos 2x sin x 0 cos 2 x sin x 0 Use the double angle identity to transform cos 2x cos 2 x to 1 2sin2 x 1 2 sin 2
sinx cos 2x 0
sinx cos 2x 0
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SOLVED 7 Cos 2x V3sin 2x On 0
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The trigonometric identities which include cos 2x are cos 2x sin 2x 1 cos2x cos 2x sin 2x and cos2x 2cos 2x 1 We can simplify these formulas and determine the The correct step is as follow cos 2x 2 sin x cos x iff cos 2x 2 sin x cos x 0 iff cos x cos x 2 sin x 0 and therefore the original equation is equivalent to the following 2
The solutions tell us to divide both sides by cos 2 so sin 2 cos 2 cos 2 cos 2 1 cos 2 and 1 cos 2 is sec 2 X 2 x 6 0 x 3 gt 2x 1 x 5 x 5 gt 0 10 1 x 10 4 sqrt 3 x 2 6 11x 6x 2 x 3 0 factor x 2 5x 6 simplify frac 2 3 frac 3 2 frac 1 4 x 2y 2x 5 x y 3 Show
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Tap for more steps tan 2x 1 0 cos 2x tan 2 x 1 0 cos 2 x Separate fractions tan 2x 1 0 1 1 cos 2x tan 2 x 1 0 1 1 cos 2 x Convert from 1 cos 2x 1 Trigonometry Solve for x sin 2x cos x cos 2x sin x 0 sin 2x cos x cos 2x sin x 0 sin 2 x cos x cos 2 x sin x 0 Simplify each term Tap for more
We know that the only way for this expression to be 0 is if sin x cos x 0 and cos 2 x 0 to cos x 0 We know both can t be possible because Given that 0 2 x2 x2 2x2 4 2x2 x2 4 2x2 Derivaattaei ole m a aritelty kun x 0 Murtolausekkeen nollakohdat ovat samat kuin sen osoittajan nollakohdat Derivaatta
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sinx cos 2x 0 - cosx C b Z 3cosx 2 dx Z 3 2 cosxdx 3 2 sinx C c Z cosx sinxdx sinx cosx C sinx cosx C 9 Funktion f integraalifunktio on F x Z 3 x 2x 1dx