2cos 2x 3cosx 1 0 Free Pre Algebra Algebra Trigonometry Calculus Geometry Statistics and Chemistry calculators step by step
Let t cosx We can thus rewrite the equation as 2t2 3t 1 0 This can be factored as follows 2t2 2t t 1 0 2t t 1 1 t 1 0 2t 1 t 1 0 t 1 2 and 1 Solve your math problems using our free math solver with step by step solutions Our math solver supports basic math pre algebra algebra trigonometry calculus and more
2cos 2x 3cosx 1 0
2cos 2x 3cosx 1 0
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Come Risolvi 2cos 2x 3cosx 1 0 E Trovi Tutte Le Soluzioni
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1 Sin 2x 3cosx 2 Sin 4x cos 4x sin 4x 3 2cos 2x 1 4sin 2x 4 2co
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How to Solve Trigonometric Equations 2cos 2x 3cosx 1 0 Solving Trig Equations Trigonometry Playlist sin 3pi 5 cos pi 15 cos 3pi 5 sin Trigonometric Factor by grouping Tap for more steps 2cos x 1 cos x 1 0 If any individual factor on the left side of the equation is equal to 0 the entire expression will be equal to 0 2cos x 1
Explanation For simplicity we let u cosx 2cos2x 3cosx 1 2u2 3u 1 2u2 3u 1 0 And you ll notice that we can split the middle term and factorize 2u2 2u u Explanation 2cos2 x 1 3cos x 1 0 2u2 3u 2 0 u 2 2u 1 0 u 2 is extraneous because cos x cannot equal 2 cos x 1 2 is the only possible root x
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By the definition of cosine function we have that cos alpha cos theta iff alpha theta 2k pi lor alpha theta 2k pi quad k in mathbb Z and thus cos 3x cos 2x iff For 0 solve for x 2cos 2x 3cosx 1 0 2cosx 1 cosx 1 0 2cosx 1 0 cosx 1 2 x 2 3 or cosx 1 cosx 1 x
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2cos 2x 3cosx 1 0 - Explanation For simplicity we let u cosx 2cos2x 3cosx 1 2u2 3u 1 2u2 3u 1 0 And you ll notice that we can split the middle term and factorize 2u2 2u u