2 cos 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 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
2 cos 2x 3cosx 1 0
2 cos 2x 3cosx 1 0
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Evaluate Sin X Cos X cos 2x 3cosx 2 dx X 0 2 Sarthaks
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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 Identities Playlist Consolidate 2 n and 2 2 n to 2 n x 3 2 n 5 3 2 n 2 n for any integer n Free math problem solver answers your algebra geometry trigonometry calculus and statistics
Set cos x 2 cos x 2 equal to 0 0 and solve for x x Tap for more steps No solution The final solution is all the values that make 2cos x 1 cos x 2 0 2 cos x 1 cos x 2 0 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 1 0 2u u
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Divide each term in 2cos 3x 1 2 cos 3 x 1 by 2 2 and simplify Tap for more steps cos 3x 1 2 cos 3 x 1 2 Take the inverse cosine of both sides of the equation to extract x x from Let y cos x Then the equation becomes 3y 2 y 2 0 This can be solved using the quadratic formula or any other method for solving quadratics The two solutions are y 1 and
Examples left begin cases 8x 2y 46 7x 3y 47 end cases right Solve your math problems using our free math solver with step by step solutions Our math solver supports Solve for n by factoring 2n2 n 4n 2 0 n 2n 1 2 2n 1 0 n 2 2n 1 0 n 2 0 n 2 2n 1 0 n 1 2 Substitute n cosx in for those two answers
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2 cos 2x 3cosx 1 0 - Use inverse trigonometric functions to find the solutions and check for extraneous solutions A basic trigonometric equation has the form sin x a cos x a tan x a cot x a The